APPENDIX C
ANALYSIS OF GENERIC SPANS FOR FORMULA B TRUCKS
This Appendix consists of the following sections:









INTRODUCTION
ANALYSIS OF GENERIC SPANS FOR CANDIDATE LOAD MODELS
COMPARE CANDIDATE LOAD MODELS TO STATE POSTING LOADS THAT
SATISFY ALL FORMULA B REQUIREMENTS
GOVERNING FORMULA B TRUCKS
PROPOSED NOTIONAL RATING LOAD MODEL
COMPARE FORCES INDUCED BY THE PROPOSED RATING TRUCK WITH
HS20 & AASHTO LEGAL LOADS
PROPOSED LEGAL LOADS FOR POSTING
COMPARISON OF RATING FACTORS
SUMMARY OF FINDINGS
INTRODUCTION
A test suite of simple and continuous span bridges were assembled and used in the analysis of load
effects. The span increments were 5 feet for spans under 100 feet and 10 feet were spans between 100 ft
and 200 ft. The longer spans are less sensitive and less vulnerable to the effects of these short heavy
trucks and a 10 ft increment was considered satisfactory for the purposes of this study without with out
compromising accuracy. The continuous spans were made up of two-span, three-span and four-span
continuous structures with span ratios selected to represent actual bridge configurations. For the two-span,
two equal spans were used. For the three-span, each end spans was set at 0.8 times the interior span. For
the four-span, the two equal end spans were 0.8 times the two equal interior spans. For the analysis of
three and four span configurations a more selective use of trucks in the suite of candidate loads was done,
omitting trucks considered unlikely to govern based on the findings of the two-span analysis.
Bridges having transverse members were also included in the test suite assembled for this purpose.
Floorbeam spacings from 10 feet to 30 feet (in one foot increments) were used in this study. The
analytical studies were done to determine the stringer live load reactions (stringers simply supported
between floorbeams) on floorbeams and caps, which were compared with reactions from the AASHTO
legal trucks. From the results it was also easy to identify the governing trucks for floorbeam and cap
ratings. As live load reaction is the key parameter that impacts load rating of transverse members, the
results of this study will expose the potential impact of the candidate load models on transverse member
ratings.
ANALYSIS OF GENERIC SPANS FOR CANDIDATE LOAD MODELS
The following series of tables and charts present the findings of the analytical studies. In the tables, the
governing load effects are shaded for easy identification. Table C-1 summarizes the results for simple and
continuous spans. Results for transverse members are given in Table C-13. In each table, the governing
FBF truck moments and shears for all spans are compiled into a single column. Ratios obtained by
dividing FBF trucks load effects by AASHTO trucks load effects provide a quick metric for the level of
bridge overstress. Charts of this overstress ratio by span length, along with charts of moments and shears,
are also given below.
C-1
TABLE C-1 Summary of Analysis Results
C-2
TABLE C-2 Simple Span Moments (Units: Ft., K-Ft)
C-3
Simple Span Moment Ratios
1.60
1.49
1.40
Moment Ratio
1.20
1.00
0.80
0.60
0.40
0.20
0.00
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100 110 120 130 140 150 160 170 180 190 200
Span (ft)
Ratio = FBF/AASHTO LEGAL
Figure C-1
Simple Span Moment Ratios
C-4
SIMPLE SPAN MOMENTS
4000.0
3500.0
MOMENT (KFT)
3000.0
2500.0
2000.0
1500.0
1000.0
500.0
0.0
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100 110 120 130 140 150 160 170 180 190 200
SPAN (FT)
T3
Figure C-2
T7B
T4A
T5A
T6A
Simple Span Moments
C-5
T7A
GOVERNING AASHTO TRUCK
TABLE C-3 Simple Span Shears (Units: Ft., K)
C-6
Simple Span Shear Ratios
1.60
1.40
1.37
1.20
Shear Ratio
1.00
0.80
0.60
0.40
0.20
0.00
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100 110 120 130 140 150 160 170 180 190 200
Span (ft)
Ratio = FBF/AASHTO LEGAL
Figure C-3 Simple Span Shear Ratios
C-7
SIMPLE SPAN SHEARS
80.0
70.0
60.0
SHEAR (K)
50.0
40.0
30.0
20.0
10.0
0.0
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100 110 120 130 140 150 160 170 180 190 200
SPAN (FT)
T3
T8
T6B
T7B
T4A
Figure C-4 Simple Span Shears
C-8
T5A
GOVERNING AASHTO TRUCK
TABLE C-4 Maximum Positive Moment  Two-Span Continuous (Units: Ft., K-Ft)
C-9
Two Equal Continuous Spans; Positive Moment Ratios
1.60
1.48
1.40
Moment Ratio
1.20
1.00
0.80
0.60
0.40
0.20
0.00
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100 110 120 130 140 150 160 170 180 190 200
Span (ft)
Ratio = FBF/AASHTO LEGAL
Figure C-5 Positive Moment Ratios  Two-Span Continuous
C-10
MAXIMUM POSITIVE MOMENT --- TWO EQUAL CONTINUOUS SPANS
3500.0
3000.0
MOMENT (K-FT)
2500.0
2000.0
1500.0
1000.0
500.0
0.0
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100 110 120 130 140 150 160 170 180 190 200
SPAN (FT)
T3
T7B
T4A
T5A
T6A
Figure C-6 Maximum Positive Moments  Two-Span Continuous
C-11
T7A
Governing AASHTO Truck
TABLE C-5 Maximum Negative Moment  Two-Span Continuous (Units: Ft., K-Ft)
C-12
Two Equal Continuous Spans; Negative Moment Ratios
1.40
1.32
1.26
1.20
Moment Ratio
1.00
0.80
0.60
0.40
0.20
0.00
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100 110 120 130 140 150 160 170 180 190 200
Span (ft)
Ratio = FBF/AASHTO LEGAL
Figure C-7 Negative Moment Ratios  Two-Span Continuous
C-13
MAXIMUM NEGATIVE MOMENT --- TWO EQUAL CONTINUOUS SPANS
0.0
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100 110 120 130 140 150 160 170 180 190 200
-200.0
-400.0
MOMENT (KFT)
-600.0
-800.0
-1000.0
-1200.0
-1400.0
-1600.0
-1800.0
SPAN (FT)
T3
T8
T4A
T5A
T6A
Figure C-8 Maximum Negative Moments  Two-Span Continuous
C-14
T7A
Governing AASHTO Truck
TABLE C-6 Maximum Shear  Two-Span Continuous (Units: Ft., K)
C-15
Two Equal Continuous Spans; Shear Ratios
1.60
1.36
1.40
1.34
1.20
Shear Ratio
1.00
0.80
0.60
0.40
0.20
0.00
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95 100 110 120 130 140 150 160 170 180 190 200
Span (ft)
Ratio = FBF/AASHTO LEGAL
Figure C-9 Shear Ratios  Two-Span Continuous
C-16
MAXIMUM SHEAR --- TWO EQUAL CONTINUOUS SPANS
90.0
80.0
70.0
SHEAR (K)
60.0
50.0
40.0
30.0
20.0
10.0
0.0
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100 110 120 130 140 150 160 170 180 190 200
SPAN (FT)
T3
T8
T4A
T5A
Figure C-10 Maximum Shear  Two-Span Continuous
C-17
T6A
T7A
Governing AASHTO
TABLE C-7 Maximum Positive Moment  Three-Span Continuous (Units: Ft., K-Ft)
C-18
THREE SPAN CONTINUOUS -- POSITIVE MOMENT RATIOS
1.60
1.48
1.40
Moment Ratio
1.20
1.00
0.80
0.60
0.40
0.20
0.00
12.5 18.8 25.0 31.3 37.5 43.8 50.0 56.3 62.5 68.8 75.0 81.3 87.5 93.8 100.0 106.3 112.5 118.8 125.0 137.5 150.0 162.5 175.0 187.5 200.0
Interior Span (ft)
Ratio = FBF/AASHTO LEGAL
Figure C-11 Positive Moment Ratios  Three-Span Continuous
C-19
TABLE C-8 Maximum Negative Moment  Three-Span Continuous (Units: Ft., K-Ft)
C-20
THREE SPAN CONTINUOUS - NEGATIVE MOMENT RATIOS
2.00
1.80
1.73
1.60
1.39
Moment Ratio
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00
12.5 18.8 25.0 31.3 37.5 43.8 50.0 56.3 62.5 68.8 75.0 81.3 87.5 93.8 100.0 106.3 112.5 118.8 125.0 137.5 150.0 162.5 175.0 187.5 200.0
Interior Span (ft)
Ratio = FBF/AASHTO LEGAL
Figure C-12 Negative Moment Ratios  Three-Span Continuous
C-21
TABLE C-9
Maximum Shear  Three-Span Continuous (Units: Ft., K)
C-22
THREE SPAN CONTINUOUS -- SHEAR RATIOS
1.60
1.40
1.35
1.20
Shear Ratio
1.00
0.80
0.60
0.40
0.20
0.00
12.5 18.8 25.0 31.3 37.5 43.8 50.0 56.3 62.5 68.8 75.0 81.3 87.5 93.8 100.0 106.3 112.5 118.8 125.0 137.5 150.0 162.5 175.0 187.5 200.0
Interior Span (ft.)
Ratio = FBF/AASHTO LEGAL
Figure C-13 Shear Ratios  Three-Span Continuous
C-23
TABLE C-10
Maximum Positive Moments  Four-Span Continuous (Units: Ft., K-Ft)
C-24
FOUR SPAN CONTINUOUS --- POSITIVE MOMENT RATIOS
1.60
1.48
1.40
Moment Ratio
1.20
1.00
0.80
0.60
0.40
0.20
0.00
12.5 18.8 25.0 31.3 37.5 43.8 50.0 56.3 62.5 68.8 75.0 81.3 87.5 93.8 100.0 106.3 112.5 118.8 125.0 137.5 150.0 162.5 175.0 187.5 200.0
Interior Span (ft.)
Ratio = FBF/AASHTO LEGAL
Figure C-14 Positive Moment Ratios  Four-Span Continuous
C-25
TABLE C-11
Maximum Negative Moments  Four-Span Continuous (Units: Ft., K-Ft)
C-26
FOUR SPAN CONTINUOUS --- NEGATIVE MOMENT RATIOS
1.60
1.40
1.34
Moment Ratio
1.20
1.00
0.80
0.60
0.40
0.20
0.00
12.5 18.8 25.0 31.3 37.5 43.8 50.0 56.3 62.5 68.8 75.0 81.3 87.5 93.8 100.0 106.3 112.5 118.8 125.0 137.5 150.0 162.5 175.0 187.5 200.0
Interior Span (ft.)
Ratio = FBF/AASHTO LEGAL
Figure C-15 Negative Moment Ratios  Four-Span Continuous
C-27
TABLE C-12
Maximum Shear  Four-Span Continuous (Units: Ft., K)
C-28
FOUR SPAN CONTINUOUS --- SHEAR RATIOS
1.60
1.40
1.34
1.20
Shear Ratio
1.00
0.80
0.60
0.40
0.20
0.00
12.5 18.8 25.0 31.3 37.5 43.8 50.0 56.3 62.5 68.8 75.0 81.3 87.5 93.8 100.0 106.3 112.5 118.8 125.0 137.5 150.0 162.5 175.0 187.5 200.0
Interior Span (ft.)
Ratio = FBF/AASHTO LEGAL
Figure C-16 Shear Ratios  Four-Span Continuous
C-29
TABLE C-13
Stringer Live Load Reactions on Transverse Members
C-30
COMPARE CANDIDATE LOAD MODELS TO STATE POSTING LOADS THAT
SATISFY ALL FORMULA B REQUIREMENTS
The previous tables and charts described the analysis results for the suite of twelve candidate FBF truck
models with 3 to 8 axles. Overstress ratios were computed that compare the governing FBF truck load
effects with that of the three AASHTO trucks (also Formula B trucks). This section reports the results of
an analytical study that compared the load effects produced by the FBF truck models with the load effects
from the State rating and posting loads that satisfy all Formula B requirements (gross weight and
consecutive axle weights). This is only a small subset of State posting loads as the most severe State
posting loads are not Formula B trucks. If trucks that only violate the inner-bridge Formula B limits were
considered, this number will increase significantly and will include the heavy multi-axle single–unit
trucks used by North Carolina and Pennsylvania (these trucks with a small reduction in axle loads will
become conforming FBF trucks).
The intent of this study is to verify that the suite of candidate FBF trucks developed will also be the
envelope vehicles for other Formula B axle configurations that are currently in current use as State legal
loads and posting loads. A total of ten such trucks that meet this criterion are shown in Fig. C-17. These
trucks have 2, 3 or 4 axles and are not particularly heavy as some of the candidate FBF loads. As
discussed, the heavier trucks with five or more axles do not meet the weight limits for consecutive axles.
Only the most severe loadings in the 2 to 4 axle configuration were considered in this analysis. The
results given in Tables C-14 thru C-17 show that the controlling candidate FBF truck models appear to
envelop the reported Formula B state posting vehicles, with the exception of a slight overstress for the 10
ft span.
C-31
Figure C-17
Formula B State Posting Loads
C-32
TABLE C-14 Simple Span Moments from Formula B Posting Loads
TABLE C-15 Simple Span Shear from Formula B Posting Loads
C-33
TABLE C-16 Two-Span Continuous ---Positive Moments from Formula B Posting
Loads
C-34
TABLE C-17 Two-Span Continuous ----- Negative Moments from Formula B Posting
Loads
GOVERNING FORMULA B TRUCKS
Maximum moments and shears for the data set of short wheelbase multi-axle trucks meeting Formula B
were calculated for the suite of simple and continuous span bridges with span ranges from 10 feet to 200
feet. The results of the analyses performed are summarized in the tables and charts given below. It is
evident that truck models T7A, T7B and T8 impose the highest load effects in most spans. In a few
instances, for very short spans under 20 feet, one of the other shorter trucks could govern, but the
governing values are not significantly higher than the maximum load effects imposed by these three
trucks. Hence, it is considered appropriate to utilize the three trucks shown below (Figure C-18)  T7A,
T7B, and T8  as envelope vehicles for all likely and reasonable Formula B trucks. These are the
heaviest Formula B trucks in the suite. They also have the most number of axles. Two of the three trucks,
T7B and T8, are vehicles governed by the 80,000 pound gross weight limit and not by Formula B limits,
which are higher. It seems logical that the three heaviest trucks in the suite with the most number of axles
are in fact the envelope vehicles. As seen in Table C-23 the difference in load effects among the three
trucks is highest in the 40 ft and under span range. This reiterates the fact that short spans are most
sensitive to axle configurations. Truck T7A also induces the highest wheel load reaction on transverse
floorbeams (see Table C-18).
C-35
T7A
11.5
8
10’
T7B
11
4’
8
9’
T8
8
6.5
4’
8
4’
10.5
6’
17
4’
17
4’
10.5
4’
17
4’
17
4’
10.5
4’
8
4’
8
11
4’
10.5
4’
Figure C-18 Envelope Vehicles for All Formula B Trucks
C-36
L = 30 ft.
GVW = 77.5 Kips
8
9.5’
10.5
4’
10.5
4’
10.5
4’
L = 34.5 ft.
GVW = 80 Kips
L = 30 ft.
GVW = 80 Kips
TABLE C-18
Live Load Reactions on Transverse Floorbeams
LIVE LOAD REACTION ON TRANSVERSE
FLOORBEAMS
Governing
Governing
STRINGER
AASHTO
Governing
FBF Truck
SPAN (FT)
Legal
FBF Truck
Reaction
Reaction
10
13.6
17.6
T7A
11
13.9
18.6
T7A
12
14.2
19.5
T7A
13
14.4
20.5
T7A
14
14.6
21.4
T7A
15
14.8
22.2
T7A
16
15.3
22.9
T7A
17
15.8
23.5
T7A
18
16.4
24.0
T7A
19
16.8
24.8
T7A
20
17.2
25.5
T7A
21
17.6
26.1
T7A
22
18.0
26.7
T7A
23
18.3
27.2
T7A
24
18.5
27.7
T7A
25
18.8
28.1
T7A
26
19.0
28.5
T7A
27
19.3
28.9
T7A
28
19.5
29.3
T7A
29
19.7
29.6
T7A
30
20.1
29.9
T7A
C-37
MAXIMUM SIMPLE SPAN MOMENTS & SHEARS
TABLE C-19 Maximum Simple Span Moments and Shears
SPAN
Governing
FBF
Moment
Governing
AASHTO
Legal
Moment
Governing
Governing
FBF Truck Governing
AASHTO
FBF Shear
for
Legal Shear
moment
10
55.8
54.4
T7A
26.7
25.5
T7B
15
108.8
95.8
T7A
33.1
28.3
T7B
20
176.2
137.7
T7A
37.3
30.1
T7B
25
253.1
179.9
T7A
41.4
34.1
T7B
30
335.2
225.8
T7A
44.7
36.8
T7B
35
417.4
287.7
T7A
48.1
38.7
T8
40
510.0
349.6
T7A
52.1
40.1
T8
45
606.8
411.7
T7A
55.2
41.4
T8
50
703.6
473.9
T7A
57.7
42.1
T8
55
800.5
536.1
T7A
59.7
47.0
T8
60
897.3
618.3
T7A
61.4
49.1
T8
65
996.3
707.1
T7B
62.8
50.8
T8
70
1096.3
796
T7B
64.0
52.3
T8
75
1196.3
885.1
T7B
65.1
54.0
T8
80
1296.3
974.3
T7B
66.0
54.8
T8
85
1396.3
1063.5
T7B
66.9
57.0
T8
90
1496.3
1152.9
T7B
67.6
56.7
T8
95
1596.3
1242.3
T7B
68.2
59.5
T8
100
1696.3
1343.0
T7B
68.8
60.5
T8
110
1896.3
1542.8
T7B
69.8
62.3
T8
120
2096.3
1742.5
T7B
70.7
63.7
T8
130
2296.3
1942.3
T7B
71.4
65.0
T8
140
2496.3
2142.2
T7B
72.0
66.1
T8
150
2696.3
2342.0
T7B
72.6
67.0
T8
160
2896.3
2541.9
T7B
73.0
67.8
T8
170
3096.3
2741.8
T7B
73.4
68.5
T8
180
3296.3
2941.7
T7B
73.8
69.2
T8
190
200
3496.3
3696.3
3141.6
3341.5
T7B
T7B
74.1
74.4
69.7
70.2
T8
T8
C-38
Governing
FBF Truck
for Shear
MAXIMUM SIMPLE SPAN MOMENTS
4000.0
3500.0
3000.0
Moment (K-FT)
2500.0
2000.0
1500.0
1000.0
500.0
0.0
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200
Span (ft.)
Governing FBF Moment
Governing AASHTO Legal Moment
MAXIMUM SIMPLE SPAN SHEAR
80.0
70.0
60.0
Shear (Kips)
50.0
40.0
30.0
20.0
10.0
0.0
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95 100 110 120 130 140 150 160 170 180 190 200
Span (ft.)
Governing FBF Shear
Figure C-19
Governing AASHTO Legal Shear
Simple Span Maximum Moment and Shear Charts
C-39
TABLE C-20 Maximum Moments and Shears -- Two Equal Continuous Spans
MAXIMUM MOMENTS & SHEARS --- TWO EQUAL CONTINUOUS SPANS
Governing
Governing Governing Governing Governing
Governing
AASHTO
AASHTO FBF Truck Governing
Governing
FBF Truck FBF Truck
AASHTO
Truck
Truck
for
FBF Truck
FBF Truck
Positive
Truck
for Neg.
Negative
Positive
Positive
Shear
for Shear
Moment
Shear
Moment
Moment
Moment
Moment
TWO
EQUAL
SPANS
Governing
FBF Truck
Negative
Moment
10
-39.0
-29.5
15
-74.0
-63.5
T8
20
-115.4
-93.3
T8
25
-147.4
-139.6
T7A
30
-185.1
-186.7
T7A
35
-218.2
-225.1
40
-247.9
45
-285.6
50
-329.7
-315.4
T8
55
-372.9
-343.2
T8
60
-415.4
-367.3
T8
65
-457.3
-388.3
T8
70
-498.7
-406.9
T8
75
-539.8
-427.4
T8
80
-580.6
-469.6
T8
85
-621.1
-515.8
T8
90
-661.4
-561.2
T8
95
-701.5
-606.0
100
-741.4
110
-820.9
120
-900.1
-823.0
T8
130
-978.8
-907.4
T8
140
-1057.3
-990.7
150
-1135.7
160
-1213.5
170
-1291.9
-1236.5
T8
180
-1369.8
-1317.4
T8
190
200
-1447.6
-1525.3
-1397.9
-1478.0
44.1
T5A
30.2
27.5
T7A
87.0
77.2
T6A
37.3
30.3
T7A
137.5
111.5
T6A
41.9
31.3
T7A
200.1
146.2
T7A
46.1
36.3
T7B
265.5
185.5
T7A
49.8
39.1
T7B
T7A
331.8
233.3
T7A
53.4
41.1
T8
-256.1
T7A
404.9
282.2
T7A
57.6
42.5
T8
-283.0
T8
481.9
331.9
T7A
60.7
44.8
T8
559.7
382.0
T7A
63.2
48.3
T8
638.1
432.5
T7A
65.1
51.0
T8
716.9
491.4
T7A
66.6
53.3
T8
795.9
560.9
T7A
67.9
55.1
T8
875.0
631.2
T7A
69.0
56.8
T8
956.7
702.2
T7B
69.9
58.8
T8
1038.7
773.6
T7B
70.7
60.5
T8
1120.8
845.4
T7B
71.3
61.9
T8
1203.1
917.6
T7B
71.9
63.2
T8
T8
1285.3
990.1
T7B
72.4
64.3
T8
-650.3
T8
1367.7
1062.8
T7B
72.9
65.3
T8
-737.4
T8
1532.6
1214.0
T7B
73.6
67.0
T8
1697.7
1376.1
T7B
74.3
68.4
T8
1862.9
1539.0
T7B
74.8
69.5
T8
T8
2028.3
1702.2
T7B
75.2
70.4
T8
-1073.3
T8
2193.7
1865.9
T7B
75.6
71.2
T8
-1155.2
T8
2359.2
2029.9
T7B
75.9
71.9
T8
2524.7
2194.1
T7B
76.2
72.4
T8
2690.2
2358.5
T7B
76.4
73.0
T8
2523.1
2687.8
T7B
T7B
76.6
76.8
73.4
73.8
T8
T8
T7A
T8
T8
44.1
2855.9
3021.5
C-40
MAXIMUM MOMENTS -- TWO EQUAL CONTINUOUS SPANS
4000.0
3000.0
Moment (K-FT)
2000.0
1000.0
0.0
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200
-1000.0
-2000.0
Span (ft.)
Governing FBF Truck Negative Moment
Governing AASHTO Truck Negative Moment
Governing FBF Truck Positive Moment
Governing AASHTO Truck Positive Moment
MAXIMUM SHEAR -- TWO EQUAL CONTINUOUS SPANS
90.0
80.0
70.0
Shear (Kips)
60.0
50.0
40.0
30.0
20.0
10.0
0.0
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95 100 110 120 130 140 150 160 170 180 190 200
Spans (ft.)
Governing FBF Truck Shear
Figure C-20
Governing AASHTO Truck Shear
Maximum Moment and Shear Charts -- Two Equal Continuous Spans
C-41
MAXIMUM MOMENTS & SHEARS --- THREE CONTINUOUS SPANS
TABLE C-21 Maximum Moments and Shears -- Three Continuous Spans
Governing
EXTERIOR
INTERIOR FBF Truck
SPANS
SPAN (FT) Negative
(FT)
Moment
Governing Governing
Governing Governing
Governing
Governing
AASHTO FBF Truck
AASHTO FBF Truck Governing
Governing
FBF Truck
AASHTO
Truck
for
Truck
for
FBF Truck
FBF Truck
Positive
Truck
Negative Negative
Positive
Positive
Shear
for Shear
Moment
Shear
Moment
Moment
Moment
Moment
10.0
12.5
-46.1
-35.4
T6A
46.9
45.4
T5A
31.4
27.9
T7A
15.0
18.8
-82.8
-70.9
T8
87.6
77.7
T6A
38.3
30.8
T7A
20.0
25.0
-127.6
-105.0
T7A
143.2
112.4
T7A
43.4
34.3
T7B
25.0
31.3
-170.6
-157.4
T7A
205.9
148.7
T7A
47.4
37.5
T7B
30.0
37.5
-211.8
-204.3
T7A
278.9
196.3
T7A
51.5
40.0
T7B
35.0
43.8
-245.0
-240.3
T7A
350.2
242.5
T7A
55.3
41.0
T8
40.0
50.0
-293.5
-271.2
T8
428.5
293.2
T7A
59.1
44.2
T8
45.0
56.3
-340.4
-302.0
T8
502.9
341.3
T7A
61.7
47.4
T8
50.0
62.5
-391.5
-334.2
T8
583.5
393.3
T7A
64.0
50.3
T8
55.0
68.8
-436.8
-360.4
T8
659.5
454.2
T7A
65.7
52.6
T8
60.0
75.0
-486.5
-384.5
T8
741.8
524.1
T7B
67.2
54.6
T8
65.0
81.3
-530.7
-421.5
T8
820.6
590.6
T7B
68.3
56.6
T8
70.0
87.5
-579.6
-475.9
T8
905.3
662.8
T7B
69.4
58.6
T8
75.0
93.8
-623.1
-524.7
T8
984.8
731.0
T7B
70.2
60.2
T8
80.0
100.0
-671.4
-577.9
T8
1070.1
804.6
T7B
70.9
61.7
T8
85.0
106.3
-714.5
-625.5
T8
1150.0
874.0
T7B
71.6
63.0
T8
90.0
112.5
-762.3
-677.6
T8
1235.7
948.6
T7B
72.1
64.2
T8
95.0
118.8
-805.1
-724.1
T8
1315.9
1021.2
T7B
72.6
65.1
T8
100.0
125.0
-852.7
-775.3
T8
1401.8
1103.9
T7B
73.1
66.1
T8
110.0
137.5
-942.5
-871.4
T8
1568.4
1265.2
T7B
73.8
67.6
T8
120.0
150.0
-1032.0
-966.3
T8
1735.3
1427.7
T7B
74.4
68.8
T8
130.0
162.5
-1121.3
-1060.3
T8
1902.5
1591.2
T7B
74.9
69.9
T8
140.0
175.0
-1210.3
-1153.4
T8
2069.8
1755.3
T7B
75.3
70.7
T8
187.5
200.0
-1299.2
-1245.8
T8
-1387.9
-1337.7
T8
1920.0
2085.2
T7B
75.7
76.0
71.5
72.1
T8
T8
150.0
160.0
2237.3
2404.9
C-42
T7B
MAXIMUM MOMENTS
3000.0
2500.0
2000.0
Moment (K-FT)
1500.0
1000.0
500.0
93
.8
10
0.
0
10
6.
3
11
2.
5
11
8.
8
12
5.
0
13
7.
5
15
0.
0
16
2.
5
17
5.
0
18
7.
5
20
0.
0
87
.5
81
.3
75
.0
68
.8
62
.5
56
.3
50
.0
43
.8
37
.5
31
.3
25
.0
18
.8
12
.5
0.0
-500.0
-1000.0
-1500.0
-2000.0
Interior Span (ft.)
Governing FBF Truck Negative Moment
Governing AASHTO Truck Negative Moment
Governing FBF Truck Positive Moment
Governing AASHTO Truck Positive Moment
80.0
70.0
60.0
Shear (Kips)
50.0
40.0
30.0
20.0
10.0
12
.5
18
.8
25
.0
31
.3
37
.5
43
.8
50
.0
56
.3
62
.5
68
.8
75
.0
81
.3
87
.5
93
.8
10
0.
0
10
6.
3
11
2.
5
11
8.
8
12
5.
0
13
7.
5
15
0.
0
16
2.
5
17
5.
0
18
7.
5
20
0.
0
0.0
Interior Span (ft.)
Governing FBF Truck Shear
Governing AASHTO Truck Shear
Figure C-21 Maximum Moment and Shear Charts -- Three Continuous Spans
C-43
TABLE C-22 Maximum Moments and Shears -- Four Continuous Spans
C-44
TABLE C-23 Maximum Simple Span Moments
Governing Ratio =
FBF
Governing Span (ft)
Moment FBF/ T8
Span (ft)
T8
10
36.8
55.8
15
76.3
108.8
20
136.5
176.2
25
207.4
253.1
30
299.3
335.2
35
391.1
417.4
40
490.5
510.0
45
590.4
606.8
50
690.3
703.6
55
790.2
800.5
60
890.1
897.3
65
990.1
996.3
70
1090.1
1096.3
75
1190.0
1196.3
1.52
1.43
1.29
1.22
1.12
1.07
1.04
1.03
1.02
1.01
1.01
1.01
1.01
1.01
T8
Governing Ratio =
FBF
Governing
Moment FBF/ T8
80
1290.0
1296.3
85
1390.0
1396.3
90
1489.9
1496.3
95
1589.9
1596.3
100
1689.9
1696.3
110
1889.8
1896.3
120
2089.8
2096.3
130
2289.8
2296.3
140
2489.8
2496.3
150
2689.8
2696.3
160
2889.7
2896.3
170
3089.7
3096.3
180
3289.7
3296.3
190
3489.7
3496.3
200
3689.7
3696.3
C-45
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
PROPOSED NOTIONAL RATING LOAD MODEL
The analytical studies have identified a single rating vehicle (80 Kips) that will envelope the load effects
of all reasonable Formula B truck configurations on simple and continuous spans ranging from 10 feet to
200 feet in length (Fig C-22). This truck meets all Formula B requirements (inner and outer) and all
Federal weight laws. This truck will be referred to herein as Truck BFT (Bridge Formula Truck). Bridges
that rate for the truck BFT are safe for all Formula B configurations, represented by the twelve FBF truck
models shown previously. A Rating Factor < 1.0 indicates that further analysis is required to determine
the need for posting. In some cases posting may not be required as the load effects of the posting loads
may be less than for the BFT.
When using truck BFT (Fig C-22), computation of load effects are to be done in accordance with the
following guidelines:
1)
2)
Axles that do not contribute to the maximum load effect shall be neglected.
The drive axle spacing can be varied from 6’ to 14’ in order to maximize force effects.
The force effects induced by the candidate rating truck BFT and the suite of twelve representative
Formula B trucks with 3 to 8 axles (Formula B trucks are denoted as FBF trucks) are compared in the
following tables and figures:
Table C-24:
Table C-25:
Table C-26:
Figure C-23:
Figure C-24:
Maximum and Minimum Ratios of Force Effects
Maximum Moments – Simple Spans (Governing FBF Truck vs. BFT)
Maximum Shear – Simple Spans (Governing FBF Truck vs. BFT)
Maximum Moments – Simple Spans (Governing FBF Truck vs. BFT)
Maximum Shear – Simple Spans (Governing FBF Truck vs. BFT)
Table C-27:
Table C-28:
Table C-29:
Figure C-25:
Figure C-26:
Figure C-27:
Maximum Positive Moments – Two-Span Cont. (Governing FBF Truck vs. BFT)
Maximum Negative Moments – Two-Span Cont. (Governing FBF Truck vs. BFT)
Maximum Shear – Two-Span Cont. (Governing FBF Truck vs. BFT)
Maximum Negative Moments – Two-Span Cont. (Governing FBF Truck vs. BFT)
Maximum Positive Moments – Two-Span Cont. (Governing FBF Truck vs. BFT)
Maximum Shear – Two-Span Cont. (Governing FBF Truck vs. BFT)
Table C-30:
Table C-31:
Table C-32:
Figure C-28:
Figure C-29:
Figure C-30:
Maximum Shear – Three-Span Cont. (Governing FBF Truck vs. BFT)
Maximum Positive Moments – Three-Span Cont. (Governing FBF Truck vs. BFT)
Maximum Negative Moments – Three-Span Cont. (Governing FBF Truck vs. BFT)
Maximum Positive Moments – Three-Span Cont. (Governing FBF Truck vs. BFT)
Maximum Negative Moments – Three-Span Cont. (Governing FBF Truck vs. BFT)
Maximum Shear – Three-Span Cont. (Governing FBF Truck vs. BFT)
Table C-33:
Table C-34:
Table C-35:
Figure C-31:
Figure C-32:
Figure C-33:
Maximum Positive Moments – Four-Span Cont. (Governing FBF Truck vs. BFT)
Maximum Shear – Four-Span Cont. (Governing FBF Truck vs. BFT)
Maximum Negative Moments – Four-Span Cont. (Governing FBF Truck vs. BFT)
Maximum Positive Moments – Four-Span Cont. (Governing FBF Truck vs. BFT)
Maximum Shear – Four-Span Cont. (Governing FBF Truck vs. BFT)
Maximum Negative Moments – Four-Span Cont. (Governing FBF Truck vs. BFT)
A number of trials were performed prior to selecting truck BFT as the best envelope vehicle for the suite
of FBF trucks. Moment and shear ratios (BFT/FBF) are also reported in the tables to facilitate easy
C-46
comparison. A ratio greater than 1.0 indicates that the proposed rating truck BFT produces a higher force
effect than the representative Formula B configurations. A desirable characteristic of the BFT truck
selected is that the moment and shear ratios for the various span lengths and span configurations are
consistently slightly above 1.0, except for a few very short continuous spans (less than 20 ft) where the
ratios were slightly below 1.0. In summary, truck BFT appears to be a very good envelope vehicle for the
suite of FBF trucks.
TABLE C-24 Maximum and Minimum Ratios of Force Effects
FORCE EFFECT
Ratio BFT/FBF: Min, Max
Maximum Moments – Simple Spans
1.00, 1.05
Maximum Shear – Simple Spans
0.99, 1.04
Maximum Positive Moments – Two-Span Cont
1.00, 1.05
Maximum Negative Moments – Two-Span Cont.
0.94, 1.04 Min @ span = 20 ft
Maximum Shear – Two-Span Cont.
1.00, 1.04
Maximum Shear – Three-Span Cont.
0.98, 1.02 Min @ span = 10 ft.
Maximum Positive Moments – Three-Span Cont.
0.99, 1.04
Maximum Negative Moments – Three-Span Cont.
0.97, 1.03 Min @ span = 10 ft
Maximum Positive Moments – Four-Span Cont.
0.90, 1.04 Min @ span = 10 ft
Maximum Shear – Four-Span Cont.
0.95, 1.03 Min @ span = 10 ft
Maximum Negative Moments – Four-Span Cont.
0.99, 1.15 Max @ span = 10 ft.
The standard truck BFT configuration (8-axle truck with 6’ drive axle spacing) will generally govern the
rating analyses of bridges. A few exceptions to this statement are evident and should be noted. In order to
maximize the BFT positive moment in very short continuous spans, certain end axles had to be omitted
during the analysis (see Tables C-27, C-31 & C-33). Typically, continuous span bridges with span lengths
less than 25 feet required the omission of one or more end axles to maximize the positive moment. For the
Formula B trucks (FBF trucks), the same force effect was governed by the 5 or 6 axle truck (T5A or
T6A). So, it is to be expected that certain axles in the BFT load model that do not contribute to the
maximum positive moments need to be neglected or they will contribute to bending in the opposite
(negative) direction. Identifying the governing axle configuration may require a few trials; not considered
particularly difficult as most continuous beam analyses are automated. This requirement should not affect
many load ratings as the population of continuous bridges with spans under 25 feet is not likely to be
significant. To guide the rating engineer the Manual commentary could explain that all simple spans and
continuous spans with spans > 25 feet would not be affected by the requirement to omit axles that do not
contribute to the maximum load effect. Axles that fall outside the bridge are not affected by this
requirement as they are automatically neglected in the analysis.
In a few cases, the drive axle spacing was also varied to increase the positive moments in short
continuous spans (see Tables C-27, C-31 & C-33). Increasing the drive axle spacing from 6 feet to 14 feet
resulted in a slight increase in positive moments for continuous span bridges with spans less than 35 feet.
Language in the commentary could guide the rating engineer as to where the variable drive axle spacing
may be important and should be evaluated.
C-47
TABLE C-25
Maximum Moments – Simple Spans
Maximum Moments -- Simple Spans
Compares Formula B Trucks (FBF) With Proposed
Rating Truck (BFT)
Simple Spans
Single Governing
FBF Truck
Span (ft.)
for
moment
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
T7A
T7A
T7A
T7A
T7A
T7A
T7A
T7A
T7A
T7A
T7A
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
FBF
Moment
BFT
Moment
Ratio =
BFT/FBF
55.8
108.8
176.2
253.1
335.2
417.4
510.0
606.8
703.6
800.5
897.3
996.3
1096.3
1196.3
1296.3
1396.3
1496.3
1596.3
1696.3
1896.3
2096.3
2296.3
2496.3
2696.3
2896.3
3096.3
3296.3
3496.3
3696.3
55.8
108.8
176.2
253.1
345.0
437.8
537.6
637.4
737.3
837.2
937.1
1037.0
1136.9
1236.9
1336.8
1436.8
1536.7
1636.7
1736.6
1936.6
2136.5
2336.5
2536.5
2736.4
2936.4
3136.4
3336.4
3536.3
3736.3
1.00
1.00
1.00
1.00
1.03
1.05
1.05
1.05
1.05
1.05
1.04
1.04
1.04
1.03
1.03
1.03
1.03
1.03
1.02
1.02
1.02
1.02
1.02
1.01
1.01
1.01
1.01
1.01
1.01
C-48
TABLE C-26 Maximum Shear–Simple Spans
Maximum Shear -- Simple Spans
Compares Formula B Trucks (FBF) With Proposed
Rating Truck (BFT)
Simple Span
Single Governing
Span (ft.) FBF Truck FBF Shear BFT Shear
for Shear
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
T7B
T7B
T7B
T7B
T7B
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
26.7
33.1
37.3
41.4
44.7
48.1
52.1
55.2
57.7
59.7
61.4
62.8
64.0
65.1
66.0
66.9
67.6
68.2
68.8
69.8
70.7
71.4
72.0
72.6
73.0
73.4
73.8
74.1
74.4
26.7
33.1
38.8
42.6
45.3
48.6
51.8
54.6
57.1
59.2
60.9
62.4
63.7
64.7
65.7
66.5
67.3
68.0
68.6
69.6
70.5
71.2
71.8
72.4
72.8
73.3
73.6
74.0
74.3
C-49
Ratio =
BFT/FBF
1.00
1.00
1.04
1.03
1.01
1.01
0.99
0.99
0.99
0.99
0.99
0.99
1.00
0.99
1.00
0.99
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
CANDIDATE RATING LOAD MODEL
TRUCK BFT
6
8
6’ to 14’
17
8
4’
4’
17
4’
8
4’
8
4’
8
GVW = 80 Kips
4’
TRUCK BFT (BRIDGE FORMULA TRUCK) REPRESENTS ALL SINGLE UNIT FORMULA B
TRUCK CONFIGURATIONS (LEGAL TRUCKS) WITH UP TO 8 AXLES. IT MEETS ALL
FORMULA B REQUIREMENTS AND FEDERAL WEIGHT LAWS.
Figure C-22 Bridge Formula Truck (BFT)
C-50
Simple Span Moment
4000.0
3500.0
3000.0
Governing FBF Moment
BFT Moment
2000.0
1500.0
1000.0
500.0
Span Length (Ft)
Figure C-23 Maximum Moments – Simple Spans
C-51
20
0
18
0
16
0
14
0
12
0
10
0
90
80
70
60
50
40
30
20
0.0
10
Moment (KFT)
2500.0
Simple Span Shear
80.0
70.0
60.0
Governing FBF Shear
BFT Shear
40.0
30.0
20.0
10.0
Span Length (Ft)
Figure C-24
Maximum Shear – Simple Spans
C-52
20
0
18
0
16
0
14
0
12
0
10
0
90
80
70
60
50
40
30
20
0.0
10
Shear (K)
50.0
TABLE C-27 Maximum Positive Moments – Two-Span Cont.
Maximum Positive Moment -- Two Span Continuous
Compares Formula B Trucks (FBF) With Proposed Rating Truck (BFT)
Two-Span Continuous Positive Moment
Governing
Each
FBF Truck Governing
Pos. Mom. BFT Axles Omitted or Drive Axle
BFT Pos.
Span (ft.)
for
FBF Pos.
Ratio =
Spacing Increased for Max
Moment
Positive
Moment
Moment
T5A
44.1
44.1
1.00
Axles 6,7 & 8 omitted for M+
15
T6A
87.0
87.0
1.00
Axles 7 & 8 omitted for M+
20
T6A
137.5
137.5
1.00
Axles 7 & 8 omitted for M+
25
T7A
200.1
200.1
1.00
Axles 8 omitted for M+
30
T7A
265.5
268.5
1.01
Drive Axle Spacing to 14'
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
T7A
331.8
345.6
1.04
Drive Axle Spacing to 14'
T7A
T7A
T7A
T7A
T7A
T7A
T7A
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
404.9
481.9
559.7
638.1
716.9
795.9
875.0
956.7
1038.7
1120.8
1203.1
1285.3
1367.7
1532.6
1697.7
1862.9
2028.3
2193.7
2359.2
2524.7
2690.2
2855.9
3021.5
425.0
505.2
586.1
667.5
749.0
830.8
912.8
995.0
1077.2
1159.5
1241.9
1324.4
1406.9
1572.0
1737.3
1902.7
2068.2
2233.7
2399.3
2564.9
2730.6
2896.3
3062.0
1.05
1.05
1.05
1.05
1.04
1.04
1.04
1.04
1.04
1.03
1.03
1.03
1.03
1.03
1.02
1.02
1.02
1.02
1.02
1.02
1.02
1.01
1.01
10
BFT/FBF
C-53
Moment
TABLE C-28 Maximum Negative Moments – Two-Span Cont.
Maximum Negative Moment -- Two Span
Continuous
Compares Formula B Trucks (FBF) With Proposed
Rating Truck (BFT)
Two-Span Continuous Negative Moment
Each
Governing
Span (ft.)
Governing
BFT Neg
Moment
Neg. Mom.
Ratio =
BFT/FBF
-39.0
-39.9
1.02
-74.0
-115.4
-147.4
-185.1
-218.2
-247.9
-285.6
-329.7
-372.9
-415.4
-457.3
-498.7
-539.8
-580.6
-621.1
-661.4
-701.5
-741.4
-820.9
-900.1
-978.8
-1057.3
-1135.7
-1213.5
-1291.9
-1369.8
-1447.6
-1525.3
-76.0
-107.9
-139.6
-180.9
-223.8
-252.1
-296.4
-339.6
-382.0
-423.8
-465.1
-506.0
-546.6
-587.0
-627.1
-667.1
-706.9
-746.6
-825.7
-904.4
-982.8
-1061.1
-1139.2
-1217.1
-1294.9
-1372.7
-1450.3
-1527.9
1.03
0.94
0.95
0.98
1.03
1.02
1.04
1.03
1.02
1.02
1.02
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
FBF Truck
FBF Neg.
for Neg.
Moment
Moment
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
T7A
T8
T8
T7A
T7A
T7A
T7A
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
C-54
TABLE C-29
Maximum Shear – Two-Span
Maximum Shear -- Two Span Continuous
Compares Formula B Trucks (FBF) With Proposed
Rating Truck (BFT)
Two Span Continuous Shear
Each
Governing
Shear
Governing
Span (ft.) FBF Truck
BFT Shear Ratio =
for Shear
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
T7A
T7A
T7A
T7B
T7B
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
FBF Shear
30.2
37.3
41.9
46.1
49.8
53.4
57.6
60.7
63.2
65.1
66.6
67.9
69.0
69.9
70.7
71.3
71.9
72.4
72.9
73.6
74.3
74.8
75.2
75.6
75.9
76.2
76.4
76.6
76.8
BFT/FBF
30.20
37.80
43.70
47.70
50.80
54.40
57.50
60.50
63.00
64.90
66.50
67.80
68.80
69.80
70.50
71.20
71.80
72.30
72.80
73.50
74.20
74.70
75.10
75.50
75.80
76.10
76.30
76.60
76.70
1.00
1.01
1.04
1.03
1.02
1.02
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
C-55
Two-Span Continuous Negative Moment
Each Span (Ft)
0.0
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200
-200.0
-400.0
-ve Moment (KFT)
-600.0
-800.0
-1000.0
-1200.0
-1400.0
-1600.0
-1800.0
Governing FBF Neg. Moment
Figure C-25 Maximum Negative Moments – Two-Span Cont.
C-56
BFT Neg Moment
Two-Span Continuous +ve Moment
3500.0
3000.0
+ve Moment (KFT)
2500.0
2000.0
Governing FBF +ve Moment
BFT +ve Moment
1500.0
1000.0
500.0
Each Span (Ft)
Figure C-26 Maximum Positive Moments – Two-Span Cont.
C-57
20
0
18
0
16
0
14
0
12
0
10
0
90
80
70
60
50
40
30
20
10
0.0
Two-Span Continuous Shear
90.0
80.0
70.0
Shear (K)
60.0
50.0
Governing FBF Shear
BFT Shear
40.0
30.0
20.0
10.0
Each Span (Ft)
Figure C-27 Maximum Shear – Two-Span Cont.
C-58
20
0
18
0
16
0
14
0
12
0
10
0
90
80
70
60
50
40
30
20
10
0.0
TABLE C-30 Maximum Shear – Three-Span
Maximum Shear -- Three Span Continuous
Compares Formula B Trucks (FBF) With Proposed
Rating Truck (BFT)
Exterior
Three Span Continuous Shear
Span (ft.) (= Governing
Governing
Shear Ratio
0.8 Interior FBF Truck
BFT Shear
FBF Shear
= BFT/FBF
for Shear
Span)
10
T7A
31.4
30.9
0.98
15
T7A
38.3
39.1
1.02
20
T7B
43.4
45
1.04
25
T7B
47.4
48.3
1.02
30
T7B
51.5
51.9
1.01
35
T8
55.3
55.5
1.00
40
T8
59.1
58.8
0.99
45
T8
61.7
61.5
1.00
50
T8
64.0
63.8
1.00
55
T8
65.7
65.5
1.00
60
T8
67.2
66.3
0.99
65
T8
68.3
68.2
1.00
70
T8
69.4
69.2
1.00
75
T8
70.2
70
1.00
80
T8
70.9
70.8
1.00
85
T8
71.6
71.4
1.00
90
T8
72.1
72
1.00
95
T8
72.6
72.5
1.00
100
T8
73.1
72.9
1.00
110
T8
73.8
73.7
1.00
120
T8
74.4
74.3
1.00
130
T8
74.9
74.8
1.00
140
T8
75.3
75.2
1.00
150
T8
75.7
75.6
1.00
160
T8
76.0
75.9
1.00
170
180
190
200
C-59
TABLE C-31 Maximum Positive Moments – Three-Span Cont.
Maximum Positive Moment -- Three Span Continuous
Compares Formula B Trucks (FBF) With Proposed Rating Truck (BFT)
Three-Span Continuous Positive Moment
Exterior
Span (ft.) Governing
FBT Axles Omitted or
FBF Truck Governing
Pos. Mom.
(= 0.8
BFT Pos.
Drive Axle Spacing
for
FBF Pos.
Ratio =
Interior
Moment
Increased for Max
Positive
Moment
BFT/FBF
Moment
Span)
Moment
T5A
46.9
46.2
0.99
15
20
T6A
87.6
93.7
1.07
T7A
143.2
147.0
1.03
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
T7A
205.9
214.2
1.04
T7A
T7A
T7A
T7A
T7A
T7A
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
278.9
350.2
428.5
502.9
583.5
659.5
741.8
820.6
905.3
984.8
1070.1
1150.0
1235.7
1315.9
1401.8
1568.4
1735.3
1902.5
2069.8
2237.3
2404.9
291.0
365.6
447.3
524.7
608.2
687.0
771.8
851.4
936.7
1016.7
1102.5
1182.9
1265.9
1349.5
1435.7
1602.8
1770.2
1937.7
2105.4
2273.1
2441.0
1.04
1.04
1.04
1.04
1.04
1.04
1.04
1.04
1.03
1.03
1.03
1.03
1.02
1.03
1.02
1.02
1.02
1.02
1.02
1.02
1.02
10
C-60
Axles 6,7 & 8 Omitted
for M+
Axles 7 & 8 Omitted for
M+
Drive axle spacing
increased to 14'
TABLE C-32 Maximum Negative Moments –Three-Span Cont.
Maximum Negative Moment -- Three Span Continuous
Compares Formula B Trucks (FBF) With Proposed Rating
Truck (BFT)
Three-Span Continuous Negative Moment
Exterior
Span (ft.) (= Governing Governing
Neg. Mom.
FBF Truck
BFT Neg
0.8 Interior
FBF Neg.
Ratio =
for Negative
Moment
Moment
BFT/FBF
Span)
Moment
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
T6A
T8
T7A
T7A
T7A
T7A
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
T8
-46.1
-82.8
-127.6
-170.6
-211.8
-245.0
-293.5
-340.4
-391.5
-436.8
-486.5
-530.7
-579.6
-623.1
-671.4
-714.5
-762.3
-805.1
-852.7
-942.5
-1032.0
-1121.3
-1210.3
-1299.2
-1387.9
-44.6
-84.6
-123.9
-165.5
-206.9
-251.1
-303.4
-349.5
-399.8
-444.5
-493.6
-537.4
-585.7
-629.0
-676.9
-719.7
-767.2
-809.8
-857.1
-946.6
-1035.8
-1124.7
-1213.5
-1302.2
-1390.7
0.97
1.02
0.97
0.97
0.98
1.02
1.03
1.03
1.02
1.02
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.00
1.00
1.00
1.00
1.00
1.00
C-61
Three Span Continuous +ve Moment
3000.0
2500.0
Moment (KFT)
2000.0
Governing FBF Pos. Moment
BFT Pos. Moment
1500.0
1000.0
500.0
90
95
10
0
11
0
12
0
13
0
14
0
15
0
16
0
80
85
70
75
60
65
50
55
40
45
30
35
20
25
10
15
0.0
Exterior Span (Ft)
Figure C-28 Maximum Positive Moments – Three-Span Cont.
C-62
Three Span Continuous -ve Moment
0.0
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
-200.0
-400.0
Moment (KFT)
-600.0
-800.0
-1000.0
-1200.0
-1400.0
-1600.0
Exterior Span (Ft)
Governing FBF Neg. Moment
Figure C-29 Maximum Negative Moments – Three-Span Cont.
C-63
BFT Neg Moment
100 110 120 130 140 150 160
Three Span Continuous Shear
80.0
70.0
60.0
Shear (K)
50.0
Governing FBF Shear
BFT Shear
40.0
30.0
20.0
10.0
95
10
0
11
0
12
0
13
0
14
0
15
0
16
0
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
0.0
Exterior Span (Ft)
Figure C-30 Maximum Shear – Three-Span Cont.
C-64
TABLE C-33 Maximum Positive Moments – Four-Span Cont.
Maximum Positive Moment -- Four Span Continuous
Compares Formula B Trucks (FBF) With Proposed Rating Truck (BFT)
Four Span Continuous
Exterior
Span (ft.) Governing
FBT Axles Omitted or
FBF Truck
Pos. Mom.
(= 0.8
FBF Pos. BFT Pos.
Drive Axle Spacing
for
Ratio =
Interior
Moment
Moment
Increased for Max
Positive
BFT/FBF
Moment
Span)
Moment
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
T5A
52.1
47.1
0.90
T6A
95.2
96.1
1.01
T7A
T7A
T7A
T7A
T7A
T7A
T7A
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
T7B
148.5
214.5
285.2
359.6
435.3
512.9
589.7
668.7
750.1
832.5
913.4
997.2
1080.1
1163.6
1245.5
1330.1
1413.6
1580.0
1751.0
1916.1
2038.8
2252.8
2422.5
148.3
220.9
293.7
373.9
451.0
534.2
613.2
697.8
777.8
863.2
943.9
1029.7
1110.7
1197.0
1278.2
1364.7
1446.1
1614.3
1782.7
1951.3
2120.0
1.00
1.03
1.03
1.04
1.04
1.04
1.04
1.04
1.04
1.04
1.03
1.03
1.03
1.03
1.03
1.03
1.02
1.02
1.02
1.02
1.04
C-65
Axles 5,6,7& 8
omitted for M+
Axles 7 & 8 omitted
for M+
TABLE C-34 Maximum Shear – Four-Span Cont.
Maximum Shear -- Four Span Continuous
Compares Formula B Trucks (FBF) With Proposed
Rating Truck (BFT)
Exterior
Four-Span Continuous
Span (ft.) Governing
Shear
(= 0.8
FBF Truck FBF Shear BFT Shear Ratio =
FBT/FBF
Interior for Shear
10
T7A
33.0
31.20
0.95
15
T7A
39.7
39.70
1.00
20
T7B
44.0
45.20
1.03
25
T7B
48.1
48.60
1.01
30
T7B
52.1
52.10
1.00
35
T8
56.3
55.90
0.99
40
T8
59.7
58.90
0.99
45
T8
62.4
61.80
0.99
50
T8
64.2
63.90
1.00
55
T8
65.9
65.80
1.00
60
T8
67.3
67.10
1.00
65
T8
68.5
68.40
1.00
70
T8
69.5
69.30
1.00
75
T8
70.3
70.20
1.00
80
T8
71.1
70.90
1.00
85
T8
71.7
71.60
1.00
90
T8
72.2
72.10
1.00
95
T8
72.7
72.60
1.00
100
T8
73.1
73.00
1.00
110
T8
73.7
73.80
1.00
120
T8
74.3
74.40
1.00
130
T8
74.8
74.90
1.00
140
T8
75.2
75.30
1.00
150
T8
75.6
160
T8
75.9
170
180
190
200
C-66
TABLE C-35 Maximum Negative Moments – Four-Span Cont.
Maximum Negative Moment -- Four Span
Continuous
Compares Formula B Trucks (FBF) With Proposed
Rating Truck (BFT)
Exterior
Four-Span Continuous
Span (ft.) Governing
Neg. Mom.
(= 0.8
FBF Truck FBF Neg. BFT Neg
Ratio =
Interior
Moment
Moment
for
BFT/FBF
Negative
Span)
10
-42.0
-48.2
1.15
T7A
15
-84.7
-88.9
1.05
T8
20
-126.2
-124.8
0.99
T8
25
-170.0
-166.2
0.98
T7A
30
-210.5
-208.5
0.99
T7A
35
-246.8
-258.3
1.05
T7A
40
-293.7
-305.9
1.04
T8
45
-344.3
-357.2
1.04
T8
50
-392.9
-403.0
1.03
T8
55
-441.8
-452.8
1.02
T8
60
-488.9
-497.5
1.02
T8
65
-536.6
-546.3
1.02
T8
70
-582.9
-590.3
1.01
T8
75
-629.9
-638.6
1.01
T8
80
-675.6
-682.1
1.01
T8
85
-722.0
-729.9
1.01
T8
90
-767.3
-773.1
1.01
T8
95
-813.4
-820.7
1.01
T8
100
-858.3
-863.6
1.01
T8
110
-948.9
-953.7
1.01
T8
120
-1043.7
-1043.5
1.00
T8
130
-1129.1
-1133.2
1.00
T8
140
-1218.8
-1222.6
1.00
T8
150
-1308.4
0.00
T8
160
-1397.8
0.00
T8
170
180
190
200
C-67
Four Span Continuous +veMoment
3000.0
2500.0
Moment (KFT)
2000.0
FBF Pos. Moment
BFT Pos. Moment
1500.0
1000.0
500.0
Exterior Span(Ft)
Figure C-31 Maximum Positive Moments – Four-Span Cont.
C-69
95
10
0
11
0
12
0
13
0
14
0
15
0
16
0
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
0.0
Four Span Continuous Shear
80.0
70.0
60.0
Shear (K)
50.0
FBF Shear
BFT Shear
40.0
30.0
20.0
10.0
0.0
10
15
20 25
30
35
40
45 50
55
60
65
70 75
80
85
Exterior Span (Ft)
Figure C-32 Maximum Shear – Four-Span Cont.
C-70
90
95 100 110 120 130 140 150 160
Four Span Continuous -ve Moment
95
10
0
11
0
12
0
13
0
14
0
15
0
16
0
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
0.0
-200.0
-400.0
Moment (KFT)
-600.0
FBF Neg. Moment
BFT Neg Moment
-800.0
-1000.0
-1200.0
-1400.0
-1600.0
Exterior Span (Ft)
Figure C-33 Maximum Negative Moments – Four-Span Cont.
C-71
COMPARE FORCES INDUCED BY THE PROPOSED RATING TRUCK (BFT) WITH
HS20 & AASHTO LEGAL LOADS
The test suite of simple and continuous span bridges (spans ranging from 10 feet to 200 feet)
were utilized to compare the force effects induced by the proposed rating truck BFT and current
AASHTO legal loads for posting to the forces produced by HS20 loading. The results are
summarized in the following tables and figures:
Table C-36:
Table C-37:
Table C-38:
Figure C-34:
Figure C-35:
Force Effect Ratios
Maximum Moments – Simple Spans (HS20, AASHTO Legal vs. BFT)
Maximum Shear – Simple Spans (HS20, AASHTO Legal vs. BFT)
Maximum Shear – Simple Spans (HS20, AASHTO Legal vs. BFT)
Maximum Moments – Simple Spans (HS20, AASHTO Legal vs. BFT)
Table C-39:
Table C-40:
Table C-41:
Figure C-36:
Figure C-37:
Figure C-38:
Maximum Negative Moments – Two-Span Cont. (HS20, AASHTO Legal, BFT)
Maximum Positive Moments – Two-Span Cont. (HS20, AASHTO Legal, BFT)
Maximum Shear – Two-Span Cont. (HS20, AASHTO Legal vs. BFT)
Maximum Positive Moments – Two-Span Cont. (HS20, AASHTO Legal, BFT)
Maximum Negative Moments – Two-Span Cont. (HS20, AASHTO Legal, BFT)
Maximum Shear – Two-Span Cont. (HS20, AASHTO Legal, BFT)
Table C-42:
Table C-43:
Table C-44:
Figure C-39:
Figure C-40:
Figure C-41:
Maximum Shear – Three-Span Cont. (HS20, AASHTO Legal, BFT)
Maximum Positive Moments – Three-Span Cont. (HS20, AASHTO Legal, BFT)
Maximum Negative Moments – Three-Span Cont.(HS20, AASHTO Legal, BFT)
Maximum Positive Moments – Three-Span Cont. (HS20, AASHTO Legal, BFT)
Maximum Negative Moments – Three-Span Cont.(HS20, AASHTO Legal, BFT)
Maximum Shear – Three-Span Cont. (HS20, AASHTO Legal , BFT)
Table C-45:
Table C-46:
Table C-47:
Figure C-42:
Figure C-43:
Figure C-44:
Maximum Positive Moments – Four-Span Cont. (HS20, AASHTO Legal, BFT)
Maximum Negative Moment – Four-Span Cont. (HS20, AASHTO Legal, BFT)
Maximum Shear – Four-Span Cont. (HS20, AASHTO Legal vs. BFT)
Maximum Positive Moments – Four-Span Cont. (HS20, AASHTO Legal, BFT)
Maximum Shear – Four-Span Cont. (HS20, AASHTO Legal vs. BFT)
Maximum Negative Moments – Four-Span Cont. (HS20, AASHTO Legal, BFT)
C-73
TABLE C-36 Force Effect Ratios
FORCE EFFECT
Maximum Moments – Simple Spans
Maximum Shear – Simple Spans
Maximum Negative Moments – Two-Span
Cont
Maximum Positive Moments – Two-Span
Cont.
Maximum Shear – Two-Span Cont.
Maximum Shear – Three-Span Cont.
Maximum Positive Moments – Three-Span
Cont.
Maximum Negative Moments – Three-Span
Cont.
Maximum Positive Moments – Four-Span
Cont.
Maximum Shear – Four-Span Cont.
Maximum Negative Moments – Four-Span
Cont.
BFT/HS20
Range of Values
0.70 to 1.22
0.88 to 1.08
0.39 to 0.98
BFT/AASHTO Legal
Range of Values
1.03 to 1.56
1.05 to 1.36
0.97 to 1.35
0.67 to 1.20
1.00 to 1.54
0.72 to 1.08
0.79 to 1.07
0.66 to 1.19
1.04 to 1.40
1.05 to 1.35
1.02 to 1.55
0.47 to 1.04
1.01 to 1.28
0.67 to 1.20
0.95 to 1.54
0.84 to 1.07
0.48 to 0.99
1.07 to 1.33
1.00 to 1.54
Some findings of these analyses are:
1. The proposed rating truck BFT consistently produces higher force effects than the current
AASHTO legal loads for the test suite of simple and continuous span bridges.
2. Simple span BFT moments are about 10% to 20% higher than HS20 for spans governed
by the HS20 truck loading. For longer spans governed by HS20 lane loading (over 170
ft), HS20 moments exceed BFT moments. BFT moments are significantly higher than
AASHTO legal loads for most simple spans (Table C-37).
3. Simple span shears for BFT and HS20 truck are within 8% for most spans (Table C-37).
4. HS20 negative moments are significantly higher than the BFT negative moments for
most continuous span configurations. The difference increases with increasing span. It
should be noted that the HS20 negative moments are governed by the lane load model,
whereas, the BFT negative moments are computed for a single truck. BFT negative
moments, however, exceed the AASHTO legal load negative moments (also computed
for a single truck).
5. BFT positive moments for most continuous spans are higher than the HS20 moments by
up to 20% (truck governs). For the same force effect, BFT exceeds the AASHTO legal
loads by over 50% in certain cases.
6. Continuous span shears for BFT and HS20 generally do not vary by more than 8%,
except when the lane load governs HS20 shear.
It should be noted that a Rating Factor < 1.0 only indicates that further analysis is required to
determine the need for posting. In some cases posting may not be required as the load effects of
the posting loads may be less than for the BFT.
C-74
TABLE C-37 Maximum Moments – Simple Spans
Maximum Moments -- Simple Spans
Compares HS20 & AASHTO Legal Trucks With Proposed Rating Truck (BFT)
Simple Span Moment (No Impact)
GOVERNING
Moment
Single
Governing
Moment
AASHTO
BFT
Ratio =
HS20
Span (ft.)
HS20
Ratio =
Moment
BFT/AASHTO
Moment
LEGAL
Loading
BFT/HS20
Legal
MOMENT
10
55.8
54.4
1.03
80.0
Truck
0.70
15
108.8
95.8
1.14
120.0
Truck
0.91
20
176.2
137.7
1.28
160.0
Truck
1.10
25
253.1
179.9
1.41
207.4
Truck
1.22
30
345.0
225.8
1.53
282.1
Truck
1.22
35
437.8
287.7
1.52
361.1
Truck
1.21
40
537.6
349.6
1.54
449.8
Truck
1.20
45
637.4
411.7
1.55
538.7
Truck
1.18
50
737.3
473.9
1.56
627.8
Truck
1.17
55
837.2
536.1
1.56
717.1
Truck
1.17
60
937.1
618.3
1.52
806.5
Truck
1.16
65
1037.0
707.1
1.47
896.0
Truck
1.16
70
1136.9
796.0
1.43
985.6
Truck
1.15
75
1236.9
885.1
1.40
1075.2
Truck
1.15
80
1336.8
974.3
1.37
1164.9
Truck
1.15
85
1436.8
1063.5
1.35
1254.6
Truck
1.15
90
1536.7
1152.9
1.33
1344.3
Truck
1.14
95
1636.7
1242.3
1.32
1434.1
Truck
1.14
100
1736.6
1343.0
1.29
1523.9
Truck
1.14
110
1936.6
1542.8
1.26
1703.5
Truck
1.14
120
2136.5
1742.5
1.23
1883.3
Truck
1.13
130
2336.5
1942.3
1.20
2063.0
Truck
1.13
140
2536.5
2142.2
1.18
2242.8
Truck
1.13
150
2736.4
2342.0
1.17
2475.0
Lane
1.11
160
2936.4
2541.9
1.16
2768.0
Lane
1.06
170
3136.4
2741.8
1.14
3077.0
Lane
1.02
180
3336.4
2941.7
1.13
3402.0
Lane
0.98
190
3536.3
3141.6
1.13
3743.0
Lane
0.94
200
3736.3
3341.5
1.12
4100.0
Lane
0.91
C-75
TABLE C-38 Maximum Shear – Simple Spans
Maximum Shear -- Simple Spans
Compares HS20 & AASHTO Legal Trucks With Proposed Rating Truck (BFT)
Simple Span Shear (No Impact)
GOVERNING
Single
AASHTO
Span (ft.) BFT Shear
LEGAL
SHEAR
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
26.7
33.1
38.8
42.6
45.3
48.6
51.8
54.6
57.1
59.2
60.9
62.4
63.7
64.7
65.7
66.5
67.3
68.0
68.6
69.6
70.5
71.2
71.8
72.4
72.8
73.3
73.6
74.0
74.3
25.5
28.3
30.1
34.1
36.8
38.7
40.1
41.4
42.1
47.0
49.1
50.8
52.3
54.0
54.8
57.0
56.7
59.5
60.5
62.3
63.7
65.0
66.1
67.0
67.8
68.5
69.2
69.7
70.2
Ratio =
BFT/AASHTO
Legal
HS20
Shear
1.05
1.17
1.29
1.25
1.23
1.26
1.29
1.32
1.36
1.26
1.24
1.23
1.22
1.20
1.20
1.17
1.19
1.14
1.13
1.12
1.11
1.10
1.09
1.08
1.07
1.07
1.06
1.06
1.06
30.4
32.0
40.0
44.8
48.4
51.8
54.3
56.3
57.8
59.1
60.2
61.1
61.9
62.6
63.2
63.7
64.1
64.5
64.9
65.6
66.1
66.6
66.9
67.3
69.1
72.3
75.6
78.8
82.0
C-76
Governing
Shear
HS20
Ratio =
Loading BFT/HS20
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Lane
Lane
Lane
Lane
Lane
0.88
1.03
0.97
0.95
0.94
0.94
0.95
0.97
0.99
1.00
1.01
1.02
1.03
1.03
1.04
1.04
1.05
1.05
1.06
1.06
1.07
1.07
1.07
1.08
1.05
1.01
0.97
0.94
0.91
Simple Span Shear
90.0
80.0
70.0
Shear (K)
60.0
50.0
BFT Shear
GOVERNING AASHTO LEGAL SHEAR
HS20 Shear
40.0
30.0
20.0
10.0
Span Length (Ft)
Figure C-34 Maximum Shear – Simple Spans
C-77
20
0
18
0
16
0
14
0
12
0
10
0
90
80
70
60
50
40
30
20
10
0.0
Simple Span Moments
4500.0
4000.0
3500.0
Moment (KFT)
3000.0
2500.0
BFT Moment
GOVERNING AASHTO LEGAL MOMENT
HS20 Moment
2000.0
1500.0
1000.0
500.0
Span Length (Ft)
Figure C-35 Maximum Moments – Simple Spans
C-78
20
0
18
0
16
0
14
0
12
0
10
0
90
80
70
60
50
40
30
20
10
0.0
TABLE C-39 Maximum Negative Moments – Two-Span Cont.
Maximum Negative Moment -- Two Span Continuous
Compares HS20 & AASHTO Legal Trucks With Proposed Rating Truck (BFT)
Two Span Continuous - Negative moment (No Impact)
Each
Span (ft.)
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
BFT Neg
Moment
-39.9
-76.0
-107.9
-139.6
-180.9
-223.8
-252.1
-296.4
-339.6
-382.0
-423.8
-465.1
-506.0
-546.6
-587.0
-627.1
-667.1
-706.9
-746.6
-825.7
-904.4
-982.8
-1061.1
-1139.2
-1217.1
-1294.9
-1372.7
-1450.3
-1527.9
HS20 Neg
Neg
Governing
Moment
Moment
HS20
(Truck or
Ratio =
Loading
Lane)
BFT/HS20
-42.6
-89.7
-123.2
-156.0
-192.6
-229.1
-265.6
-316.7
-371.7
-430.7
-493.7
-560.7
-631.6
-706.5
-785.3
-868.2
-954.9
-1045.7
-1140.5
-1341.8
-1559.1
-1792.2
-2041.3
-2306.2
-2586.9
-2883.6
-3196.2
-3524.6
-3868.9
Lane
Truck
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
0.94
0.85
0.88
0.89
0.94
0.98
0.95
0.94
0.91
0.89
0.86
0.83
0.80
0.77
0.75
0.72
0.70
0.68
0.65
0.62
0.58
0.55
0.52
0.49
0.47
0.45
0.43
0.41
0.39
C-79
AASHTO
legal Neg
Moment
Neg Moment
Ratio =
BFT/AASHTO
legal
-29.5
-63.5
-93.3
-139.6
-186.7
-225.1
-256.1
-283.0
-315.4
-343.2
-367.3
-388.3
-406.9
-427.4
-469.6
-515.8
-561.2
-606.0
-650.3
-737.4
-823.0
-907.4
-990.7
-1073.3
-1155.2
-1236.5
-1317.4
-1397.9
-1478.0
1.35
1.20
1.16
1.00
0.97
0.99
0.98
1.05
1.08
1.11
1.15
1.20
1.24
1.28
1.25
1.22
1.19
1.17
1.15
1.12
1.10
1.08
1.07
1.06
1.05
1.05
1.04
1.04
1.03
TABLE C-40 Maximum Positive Moments – Two-Span Cont.
Maximum Positive Moment -- Two Span Continuous
Compares HS20 & AASHTO Legal Trucks With Proposed Rating Truck (BFT)
Two Span Continuous - Positive Moment (No Impact)
Each
BFT Pos.
Span (ft.)
Moment
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
HS20 Pos
Pos Moment
Governing Pos Moment AASHTO
Moment
Ratio =
HS20
Ratio =
legal Pos
(Truck or
BFT/AASHTO
Loading
BFT/HS20
Moment
Lane)
legal
44.1
66.0
Truck
0.67
44.1
1.00
87.0
137.5
200.1
268.5
345.6
425.0
505.2
586.1
667.5
749.0
830.8
912.8
995.0
1077.2
1159.5
1241.9
1324.4
1406.9
1572.0
1737.3
1902.7
2068.2
2233.7
2399.3
2564.9
2730.6
2896.3
3062.0
99.0
132.0
172.4
229.1
288.3
358.7
429.1
500.9
573.3
645.8
718.3
790.7
864.5
938.2
1011.9
1085.6
1159.3
1233.1
1380.5
1527.9
1675.4
1822.8
1971.4
2153.7
2391.9
2642.3
2904.8
3179.5
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Lane
Lane
Lane
Lane
Lane
0.88
1.04
1.16
1.17
1.20
1.18
1.18
1.17
1.16
1.16
1.16
1.15
1.15
1.15
1.15
1.14
1.14
1.14
1.14
1.14
1.14
1.13
1.13
1.11
1.07
1.03
1.00
0.96
77.2
111.5
146.2
185.5
233.3
282.2
331.9
382
432.5
491.4
560.9
631.2
702.2
773.6
845.4
917.6
990.1
1062.8
1214
1376.1
1539
1702.2
1865.9
2029.9
2194.1
2358.5
2523.1
2687.8
1.13
1.23
1.37
1.45
1.48
1.51
1.52
1.53
1.54
1.52
1.48
1.45
1.42
1.39
1.37
1.35
1.34
1.32
1.29
1.26
1.24
1.22
1.20
1.18
1.17
1.16
1.15
1.14
C-80
BFT Axles Omitted or Drive
Axle Spacing Increased for
Max Moment
Axles 6,7 & 8 omitted for M+
Axles 7 & 8 omitted for M+
Axles 7 & 8 omitted for M+
Axles 8 omitted for M+
Drive Axle Spacing to 14'
Drive Axle Spacing to 14'
TABLE C-41 Maximum Shear – Two-Span Cont.
Maximum Shear -- Two Span Continuous
Compares HS20 & AASHTO Legal Trucks With Proposed Rating Truck (BFT)
Two Span Continuous - Shear (No Impact)
Each
Span (ft.) BFT Shear HS20 Shear
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
30.20
37.80
43.70
47.70
50.80
54.40
57.50
60.50
63.00
64.90
66.50
67.80
68.80
69.80
70.50
71.20
71.80
72.30
72.80
73.50
74.20
74.70
75.10
75.50
75.80
76.10
76.30
76.60
76.70
32.0
34.8
44.3
49.6
52.9
56.3
58.7
60.6
62.0
63.1
64.1
64.8
65.5
66.0
66.4
66.8
67.1
67.5
67.7
69.9
73.9
77.9
81.9
85.9
89.9
93.9
97.9
101.9
105.9
Governing
HS20
Loading
Shear
Ratio =
BFT/HS20
AASHTO
legal
Shear
Shear Ratio =
BFT/AASHTO
Legal
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
0.94
1.09
0.99
0.96
0.96
0.97
0.98
1.00
1.02
1.03
1.04
1.05
1.05
1.06
1.06
1.07
1.07
1.07
1.08
1.05
1.00
0.96
0.92
0.88
0.84
0.81
0.78
0.75
0.72
27.5
30.3
31.3
36.3
39.1
41.1
42.5
44.8
48.3
51.0
53.3
55.1
56.8
58.8
60.5
61.9
63.2
64.3
65.3
67.0
68.4
69.5
70.4
71.2
71.9
72.4
73.0
73.4
73.8
1.10
1.25
1.40
1.31
1.30
1.32
1.35
1.35
1.30
1.27
1.25
1.23
1.21
1.19
1.17
1.15
1.14
1.12
1.11
1.10
1.08
1.07
1.07
1.06
1.05
1.05
1.05
1.04
1.04
C-81
Two-Span Continuous + ve Moment
3500.0
3000.0
+ ve Moment (KFT)
2500.0
2000.0
BFT +ve Moment
HS20 +ve Moment
AASHTO Legal +ve Moment
1500.0
1000.0
500.0
Each Span (Ft)
Figure C-36 Maximum Positive Moments – Two-Span Cont.
C-82
20
0
18
0
16
0
14
0
12
0
10
0
90
80
70
60
50
40
30
20
10
0.0
Two-Span Continuous -ve Moment
Each Span (Ft)
0.0
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200
-500.0
-1000.0
Moment (KFT)
-1500.0
-2000.0
-2500.0
-3000.0
-3500.0
-4000.0
-4500.0
BFT -ve Moment
HS20 -ve Moment
Figure C-37 Maximum Negative Moments – Two-Span Cont.
C-83
AASHTO Legal -ve Moment
Two-Span Continuous Shear
120.00
100.00
Shear (K)
80.00
BFT Shear
HS20 Shear
AASHTO legal Shear
60.00
40.00
20.00
Each Span (Ft)
Figure C-38 Maximum Shear – Two-Span Cont.
C-84
20
0
18
0
16
0
14
0
12
0
10
0
90
80
70
60
50
40
30
20
10
0.00
TABLE C-42 Maximum Shear – Three-Span Cont.
Maximum Shear -- Three Span Continuous
Compares HS20 & AASHTO Legal Trucks With Proposed Rating Truck (BFT)
Three Span Continuous -- Shear (No Impact)
Exterior
Span (ft.) (=
Governing
Shear
AASHTO Shear Ratio =
HS20
0.8 Interior BFT Shear
HS20
Ratio =
legal
BFT/AASHTO
Shear
Loading BFT/HS20
Shear
Legal
Span)
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
30.9
39.1
45
48.3
51.9
55.5
58.8
61.5
63.8
65.5
66.3
68.2
69.2
70
70.8
71.4
72
72.5
72.9
73.7
74.3
74.8
75.2
75.6
75.9
32.0
39.2
46.3
50.7
54.5
57.4
59.5
61.2
62.5
63.6
64.4
65.1
65.6
66.1
66.6
66.9
67.3
67.7
69.9
74.3
78.7
83.1
87.5
91.9
96.3
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
0.97
1.00
0.97
0.95
0.95
0.97
0.99
1.00
1.02
1.03
1.03
1.05
1.05
1.06
1.06
1.07
1.07
1.07
1.04
0.99
0.94
0.90
0.86
0.82
0.79
C-85
27.9
30.8
34.3
37.5
40.0
41.0
44.2
47.4
50.3
52.6
54.6
56.6
58.6
60.2
61.7
63.0
64.2
65.1
66.1
67.6
68.8
69.9
70.7
71.5
72.1
1.11
1.27
1.31
1.29
1.30
1.35
1.33
1.30
1.27
1.25
1.21
1.20
1.18
1.16
1.15
1.13
1.12
1.11
1.10
1.09
1.08
1.07
1.06
1.06
1.05
TABLE C-43 Maximum Positive Moments – Three-Span Cont.
Maximum Positive Moment -- Three Span Continuous
Compares HS20 & AASHTO Legal Trucks With Proposed Rating Truck (BFT)
Exterior
Span (ft.)
(= 0.8
BFT Pos.
Interior
Moment
Span)
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
Three Span Continuous -- Positive Moment (No Impact)
HS20 Pos
Pos
Governing
Moment
Moment
HS20
(Truck or
Ratio =
Loading
Lane)
BFT/HS20
Pos
AASHTO
Moment
legal Pos
Ratio =
Moment BFT/AASH
TO legal
46.2
69.7
Truck
0.66
45.4
1.02
93.7
147.0
103.5
132.8
Truck
Truck
0.91
1.11
77.7
112.4
1.21
1.31
214.2
182.2
Truck
1.18
148.7
1.44
291.0
365.6
447.3
524.7
608.2
687.0
771.8
851.4
936.7
1016.7
1102.5
1182.9
1265.9
1349.5
1435.7
1602.8
1770.2
1937.7
2105.4
2273.1
2441.0
243.9
310.3
378.5
449.9
520.3
591.6
664.6
739.3
813.0
887.6
961.3
1035.9
1109.6
1184.2
1257.9
1406.2
1557.1
1708.6
1925.0
2169.2
2427.7
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Lane
Lane
Lane
1.19
1.18
1.18
1.17
1.17
1.16
1.16
1.15
1.15
1.15
1.15
1.14
1.14
1.14
1.14
1.14
1.14
1.13
1.09
1.05
1.01
196.3
242.5
293.2
341.3
393.3
454.2
524.1
590.6
662.8
731.0
804.6
874.0
948.6
1021.2
1103.9
1265.2
1427.7
1591.2
1755.3
1920.0
2085.2
1.48
1.51
1.53
1.54
1.55
1.51
1.47
1.44
1.41
1.39
1.37
1.35
1.33
1.32
1.30
1.27
1.24
1.22
1.20
1.18
1.17
C-86
BFT Axles Omitted or Drive
Axle Spacing Increased for
Max Moment
Axles 6,7 & 8 Omitted for M+
Axles 7 & 8 Omitted for M+
Drive axle spacing increased
to 14'
TABLE C-44 Maximum Negative Moments – Three-Span Cont.
Maximum Negative Moment -- Three Span Continuous
Compares HS20 & AASHTO Legal Trucks With Proposed Rating Truck (BFT)
Exterior
Span (ft.)
(= 0.8
Interior
Span)
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
Three Span Continuous -- Negative Moment (No Impact)
BFT Neg
Moment
HS20 Neg
Moment
(Truck or
Lane)
-44.6
-84.6
-123.9
-165.5
-206.9
-251.1
-303.4
-349.5
-399.8
-444.5
-493.6
-537.4
-585.7
-629.0
-676.9
-719.7
-767.2
-809.8
-857.1
-946.6
-1035.8
-1124.7
-1213.5
-1302.2
-1390.7
-45.6
-96.9
-130.7
-167.9
-205.8
-240.6
-293.1
-350.7
-412.4
-479.3
-550.2
-626.4
-706.4
-791.8
-881.0
-975.7
-1074.1
-1178.0
-1285.6
-1515.5
-1763.8
-2030.6
-2315.8
-2619.4
-2941.4
Governing Neg Moment AASHTO
HS20
Ratio =
legal Neg
Loading
BFT/HS20
Moment
Lane
Truck
Truck
Truck
Truck
Truck
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
C-87
0.98
0.87
0.95
0.99
1.01
1.04
1.04
1.00
0.97
0.93
0.90
0.86
0.83
0.79
0.77
0.74
0.71
0.69
0.67
0.62
0.59
0.55
0.52
0.50
0.47
-35.4
-70.9
-105.0
-157.4
-204.3
-240.3
-271.2
-302.0
-334.2
-360.4
-384.5
-421.5
-475.9
-524.7
-577.9
-625.5
-677.6
-724.1
-775.3
-871.4
-966.3
-1060.3
-1153.4
-1245.8
-1337.7
Neg Moment
Ratio =
BFT/AASHTO
legal
1.26
1.19
1.18
1.05
1.01
1.04
1.12
1.16
1.20
1.23
1.28
1.27
1.23
1.20
1.17
1.15
1.13
1.12
1.11
1.09
1.07
1.06
1.05
1.05
1.04
Three Span Continuous +ve Moment
3000.0
2500.0
Moment (Ft)
2000.0
BFT Pos. Moment
HS20 Pos Moment (Truck or Lane)
AASHTO legal Pos Moment
1500.0
1000.0
500.0
Exterior Span (Ft)
Figure C-39 Maximum Positive Moments – Three-Span Cont.
C-88
16
0
14
0
12
0
10
0
90
80
70
60
50
40
30
20
10
0.0
Three Span Continuous -ve Moment
Exterior Span(Ft)
16
0
14
0
12
0
10
0
90
80
70
60
50
40
30
20
10
0.0
-500.0
Moment(KFT)
-1000.0
-1500.0
BFT Neg Moment
HS20 Neg Moment (Truck or Lane)
AASHTO legal Neg Moment
-2000.0
-2500.0
-3000.0
-3500.0
Figure C-40 Maximum Negative Moments – Three-Span Cont.
C-89
Three Span Continuous: Shear
120
100
Shear(K)
80
BFT Shear
HS20 Shear
AASHTO legal Shear
60
40
20
0
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160
Exterior Span(Ft)
Figure C-41 Maximum Shear – Three-Span Cont.
C-90
TABLE C-45 Maximum Positive Moments – Four-Span
Maximum Positive Moment -- Four Span Continuous
Compares HS20 & AASHTO Legal Trucks With Proposed Rating Truck (BFT)
Four Span Continuous -- Positive Moment (No Impact)
Exterior Span
HS20 Pos
Pos
Pos Moment
Governing
AASHTO
(ft.) (= 0.8
BFT Pos.
Moment
Moment
Ratio =
HS20
legal Pos
Interior Span) Moment (Truck or
Ratio =
BFT/AASHTO
Lane)
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
47.1
96.1
148.3
220.9
293.7
373.9
451.0
534.2
613.2
697.8
777.8
863.2
943.9
1029.7
1110.7
1197.0
1278.2
1364.7
1446.1
1614.3
1782.7
1951.3
2120.0
70.2
104.0
132.9
183.6
245.9
313.0
381.7
453.7
524.6
596.5
670.0
745.2
819.3
894.4
968.5
1043.7
1117.8
1193.0
1267.0
1416.3
1568.1
1772.2
2014.3
2271.4
2543.7
Loading
BFT/HS20
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Truck
Lane
Lane
Lane
Lane
C-91
0.67
0.92
1.12
1.20
1.19
1.19
1.18
1.18
1.17
1.17
1.16
1.16
1.15
1.15
1.15
1.15
1.14
1.14
1.14
1.14
1.14
1.10
1.05
Moment
49.6
76.3
114.9
153.6
199.6
247.7
297.0
346.8
397.7
458.7
527.5
597.1
665.9
737.9
810.6
883.0
953.9
1033.3
1114.4
1274.9
1444.0
1603.6
1767.5
1934.0
2102.1
legal
0.95
1.26
1.29
1.44
1.47
1.51
1.52
1.54
1.54
1.52
1.47
1.45
1.42
1.40
1.37
1.36
1.34
1.32
1.30
1.27
1.23
1.22
1.20
0.00
0.00
TABLE C-46 Maximum Negative Moment – Four-Span Cont.
Maximum Negative Moment -- Four Span Continuous
Compares HS20 & AASHTO Legal Trucks With Proposed Rating Truck (BFT)
Four Span Continuous -- Negative Moment (No Impact)
Exterior
Span (ft.) (=
0.8 Interior
Span)
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
BFT Neg
Moment
-48.2
-88.9
-124.8
-166.2
-208.5
-258.3
-305.9
-357.2
-403.0
-452.8
-497.5
-546.3
-590.3
-638.6
-682.1
-729.9
-773.1
-820.7
-863.6
-953.7
-1043.5
-1133.2
-1222.6
HS20 Neg
Moment
(Truck or
Lane)
Governing
HS20
Loading
Neg Moment
Ratio =
BFT/HS20
AASHTO
legal Neg
Moment
Neg Moment
Ratio =
BFT/AASHTO
legal
-52.6
-99.7
-136.6
-175.5
-214.2
-261.1
-318.7
-382.4
-450.4
-524.6
-602.8
-687.5
-776.1
-871.3
-970.2
-1075.8
-1185.1
-1301.2
-1420.7
-1677.2
-1954.5
-2252.6
-2571.4
-2911.1
-3271.6
Truck
Truck
Truck
Truck
Truck
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
Lane
0.92
0.89
0.91
0.95
0.97
0.99
0.96
0.93
0.89
0.86
0.83
0.79
0.76
0.73
0.70
0.68
0.65
0.63
0.61
0.57
0.53
0.50
0.48
-31.3
-69.6
-109.0
-164.2
-208.9
-242.4
-275.6
-311.4
-341.4
-367.5
-389.8
-427.0
-478.9
-531.2
-581.8
-632.9
-682.3
-732.3
-780.8
-877.7
-978.0
-1068.0
-1161.8
-1254.9
-1374.5
1.54
1.28
1.14
1.01
1.00
1.07
1.11
1.15
1.18
1.23
1.28
1.28
1.23
1.20
1.17
1.15
1.13
1.12
1.11
1.09
1.07
1.06
1.05
0.00
0.00
C-92
TABLE C-47 Maximum Shear – Four-Span Cont.
Maximum Shear -- Four Span Continuous
Compares HS20 & AASHTO Legal Trucks With Proposed Rating Truck (BFT)
Exterior
Four Span Continuous -- Shear (No Impact)
Span (ft.)
Governing
AASHTO Shear Ratio =
HS20
Shear Ratio =
(= 0.8
BFT Shear
HS20
legal
BFT/AASHTO
Shear
BFT/HS20
Loading
Shear
Legal
Interior
10
31.20
32.8
Truck
0.95
29.2
1.07
15
39.70
39.4
Truck
1.01
31.5
1.26
20
45.20
46.4
Truck
0.97
34.8
1.30
25
48.60
50.8
Truck
0.96
38.1
1.28
30
52.10
54.6
Truck
0.95
40.4
1.29
35
55.90
57.5
Truck
0.97
42.0
1.33
40
58.90
59.6
Truck
0.99
44.7
1.32
45
61.80
61.3
Truck
1.01
48.0
1.29
50
63.90
62.6
Truck
1.02
50.5
1.27
55
65.80
63.6
Truck
1.03
52.8
1.25
60
67.10
64.4
Truck
1.04
54.7
1.23
65
68.40
65.1
Truck
1.05
56.9
1.20
70
69.30
65.7
Truck
1.05
58.8
1.18
75
70.20
66.2
Truck
1.06
60.5
1.16
80
70.90
66.6
Truck
1.06
61.9
1.15
85
71.60
67.0
Truck
1.07
63.2
1.13
90
72.10
67.3
Truck
1.07
64.3
1.12
95
72.60
68.9
Lane
1.05
65.3
1.11
100
73.00
71.1
Lane
1.03
66.2
1.10
110
73.80
75.6
Lane
0.98
67.4
1.09
120
74.40
80.2
Lane
0.93
68.8
1.08
130
74.90
84.7
Lane
0.88
69.8
1.07
140
75.30
89.2
Lane
0.84
70.6
1.07
150
93.7
Lane
71.4
0.00
160
98.2
Lane
72.0
0.00
170
180
190
200
C-93
Four Span Continuous +veMoment
3000.0
2500.0
Moment (KFT)
2000.0
BFT Pos. Moment
HS20 Pos Moment (Truck or Lane)
AASHTO legal Pos Moment
1500.0
1000.0
500.0
0.0
10
20
30
40
50
60
70
80
90
0
10
0
12
Exterior Span (Ft)
Figure C-42 Maximum Positive Moments – Four-Span Cont.
C-94
0
14
0
16
Four Span Continuos Shear
120.00
100.00
Shear (K)
80.00
BFT Shear
HS20 Shear
AASHTO legal Shear
60.00
40.00
20.00
Exterior Span (K)
Figure C-43 Maximum Shear – Four-Span Cont.
C-95
16
0
12
0
13
0
14
0
15
0
95
10
0
11
0
90
80
85
75
70
65
55
60
50
45
35
40
30
25
15
20
10
0.00
Four Span Continuous -veMoment
Exterior Span(Ft)
16
0
14
0
12
0
10
0
90
80
70
60
50
40
30
20
10
0.0
-500.0
Moment (KFT)
-1000.0
-1500.0
BFT Neg Moment
HS20 Neg Moment (Truck or Lane)
AASHTO legal Neg Moment
-2000.0
-2500.0
-3000.0
-3500.0
Figure C-44 Maximum Negative Moments – Four-Span Cont.
C-96
PROPOSED LEGAL LOADS FOR POSTING
While a single envelope rating vehicle can provide considerable simplification of load rating
computations and establish posting eligibility, it may not be the ideal solution for all posting situations. A
linear ratio of posting weights and ratings may not suffice (not conservative), as the moment effects per
unit weight may be different for different axle configurations.
Another issue to be considered is that certain multi-axle configurations that cause the highest load effects
appear to be common only in some States, and they should not lead to reduced postings in all States.
Setting weight limits for posting often requires the evaluator to determine safe load capacities for
commercial truck types that operate within a given State, in accordance with State posting practices.
Additional AASHTO legal loads for posting may be needed to give more accurate posting values.
Two options were investigated for selecting the proposed legal loads for posting:
Option 1: Includes the worst 4-axle (T4A), worst 5-axle (T5A), worst 6-axle (T6A) and worst 7axle (T7A) trucks as shown in Fig. C-45. (7-axle is also representative of 8-axle trucks)
Option 2: Includes the worst 4-axle truck (T4A), and uses truck T5A as a single representative
truck for Formula B truck configurations with 5 to 8 axles (Fig. C-46).
Under Option 1, for bridges that do not rate for truck BFT (RF < 1.0), the rating engineer will perform a
posting analysis to establish the need for posting and the posting load limit using posting loads (selected
from the suite of four trucks) representative of commercial trucks operating within the State. For instance,
if a State does not have six or seven axle SHVs in the normal traffic stream then only T4A and T5A will
be used in the posting analysis. Posting signs can show a load limit for each truck type (4-axle, 5-axle,
etc.) or a single tonnage (governing) for all multi-axle single-unit trucks.
Further simplification of the posting analysis is possible if certain posting loads could be eliminated
thereby reducing the number of new posting loads. If it can be shown that a smaller subset of these four
posting load models will consistently produce the governing posting load then a procedure is available to
eliminate certain load models from the posting analysis.
The analytical approach given below shows that the posting load remains unchanged, irrespective of truck
weight and configuration, if a set of posting loads produce the same moment (or shear) per unit weight of
truck. In other words, the truck that produces the highest moment or shear per unit weight will govern the
posting value (result in the lowest weight limit).
C-97
DETERMINING THE GOVERNING TRUCK MODEL FOR LOAD POSTING OF
BRIDGES
Posting Load = RF X W
RF 
(W= Truck Weight)
Capacity   DL
 L LL
 Capacity   DL 
PostingLoad  


L LL/W


 Capacity   DL 
PostingLoad  
W

 L LL


 AvailableLiveLoadCapacity 
PostingLoad  

  L(MomentPerUnitWeight) 
 AvailableLiveLoadCapacity 
PostingLoad  

  L(ShearPerUnitWeight) 
C-98
The available live load capacity for a bridge is a constant. The truck that produces the highest moment (or
shear) per unit weight of truck will have the lowest weight limit for posting. This could be used to
identify the critical truck for the posting analysis.
This posting load characteristic is valid provided the span moments and shears result from truck loads and
not axle loads, as in the case of very short spans. For very short spans (spans < 30 ft) the shorter trucks
will always govern posting. To illustrate this, posting loads were determined for two bridges: 1) A 65 ft
simple span bridge, 2) A 25 ft simple span bridge. The posting loads for these bridges are as follows:
TABLE C-48 Posting Loads for Truck Types
Span
Load Model
65 ft Simple Span
HS20
65 ft Simple Span
Type 3
65 ft Simple Span
Type 3S2
65 ft Simple Span
Type 3-3
65 ft Simple Span
T4A
65 ft Simple Span
T5A
65 ft Simple Span
T6A
65 ft Simple Span
T7A
65 ft Simple Span
Truck BFT
25 ft Simple Span
25 ft Simple Span
25 ft Simple Span
25 ft Simple Span
25 ft Simple Span
25 ft Simple Span
25 ft Simple Span
25 ft Simple Span
25 ft Simple Span
HS20
Type 3
Type 3S2
Type 3-3
T4A
T5A
T6A
T7A
Truck BFT
Posting Load (Kips)
95.8
90.0
121.0
146.4
85.9
89.9
90.4
92.2
92.0
69.8
55.5
84.2
108.0
50.8
53.9
56.3
61.2
63.2
The short truck T4A has the lowest posting value in both examples. For the 65 ft span the posting loads
for T5A, T6A, and T7A are nearly equal. For the 25 ft span, which is mostly governed by axle loads,
there is greater separation in the SHV posting loads with the shorter trucks T4A and T5A having weight
limits significantly lower than that for T7A and BFT.
The moments induced per unit weight of each truck for the various span lengths are given in the following
tables:
Table C-49:
Table C-50:
Table C-51:
Moment per Unit Weight -- Simple Spans
Negative Moment per Unit Weight -- Two Span Continuous
Positive Moment per Unit Weight – Two Span Continuous
Some findings from these tables and charts are:
 All Formula B trucks included in these analyses have similar moment per unit weight profiles
resulting in nearly parallel curves (Figs. C-47).
 T4A consistently generates the highest moment per unit weight for all span lengths.
C-99
 Of the other trucks with 5 to 8 axles T5A would be the most critical for posting, though the
differences in the moment per unit weight values for trucks T5A, T6A, T7A and BFT for
spans greater than 40 feet are very small (under 5%). For spans under 40 feet, the differences
are larger and are quite sensitive to span lengths.
If it is desirable to reduce the number of posting loads to simplify the posting analysis then it would be
appropriate to select T4A and T5A as the candidate posting loads. This is designated as the second option
for the selection of posting loads:
Option 2: Includes the worst 4-axle truck (T4A), and uses truck T5A as a single representative
truck for Formula B truck configurations with 5 to 8 axles (Fig. C-46).
T4A is a very common short hauling vehicle in most States (tri-axle dump truck) and would be a suitable
posting load for use nationally. Many States already use such a vehicle as a State legal load (not all satisfy
Formula B). As discussed previously, T4A would govern the posting and some States such as CT & AL
use a truck symbol to post specifically for these trucks. In the posting analysis T5A will serve as a single
representative truck for Formula B configurations with 5 to 8 axles. The posting weight limit determined
for T5A will apply to all single unit trucks with 5 or more axles. The posting sign could note this using
text.
A State may also choose the T4A posting load to apply to all single unit trucks to further simplify the
signing. Each simplification will introduce added conservatism in posting.
Note that the comparison of moments per unit weight assumes that the live load factor is the same for all
posting load models. Calibration may lead to different load factors for each truck model due to
differences in volumes and moment ratios. More precise posting evaluation is possible in LRFR using
targeted load factors for a suite of posting loads.
Another issue to be considered is the posting analysis is the likely “unbalancing” of the axle loads for a
posted truck. The loads on a posted truck may not be placed in the same proportion as a fully loaded truck
assumed in the analysis, which may affect the load effects induced per unit weight.
Further simplification of the posting analysis is considered possible if certain posting loads could be
eliminated thereby reducing the number of new posting loads (Option 2). It is shown in this section that
for bridges governed by truck loads (not axle loads) the posting weight limit remains unchanged
(irrespective of truck weight and configuration) when trucks produce the same moment (or shear) per unit
weight. Or, the truck that produces the highest moment or shear per unit weight will govern the posting
value. If it is desirable to reduce the number of posting loads to simplify the posting analysis then it
would be appropriate to select T4A and T5A as the candidate posting loads (using truck T5A as a single
representative truck for Formula B truck configurations with 5 to 8 axles). These trucks exhibit the
highest moment & shear per unit weight. This simplification will introduce added conservatism and less
flexibility in posting. Option 2 is particularly appealing to States that post bridges for a single tonnage.
Panel review comments showed that there was no clear favorite for the posting load choices. This is
understandable as the choice of posting loads is contingent on posting and signing practices and the use of
truck symbols on posting signs. There is little uniformity here. The survey of States done for this project
revealed that of the 48 States responding 32 use truck symbols on posting signs. These States may favor
more posting load choices to allow more selective use of truck symbols and weight limits. As Option 2 is
a subset of Option 1, all four candidate posting loads are being carried forward through the remaining
tasks.
C-100
Analytical studies discussed in this report provides additional data to support the selection of the posting
load models. Using T5A as a single posting vehicle for all Formula B trucks having 5 thru 8 axles has
advantages in its simplicity, and some disadvantages as outlined below:
1. A bridge span may have a Rating Factor of greater than 1.0 for T5A, but may not rate (RF < 1.0)
for the worst six, seven and eight axle trucks. This will lead to a situation where the T5A is being
used to determine a posting load for a bridge even though the bridge has adequate capacity for the
T5A truck. The concern here is whether it will cause confusion in the minds of the rating
engineers when implementing the new rating and posting loads and procedures. Theoretically, the
simplification of using T5A as a single representative posting load for a series of trucks presents a
valid approach if practical difficulties are not considered a problem.
2. T5A as a single posting vehicle works quite well for spans over 40 ft governed by the full truck
load. For very short spans where only a portion of the truck may be on the bridge, the posting
values obtained using T5A may be too conservative (over 20% less) to be considered an
acceptable simplification, especially when load restrictions are involved.
3. States that do not see all the multi-axle Formula B vehicle configurations represented by T5A, for
posting purposes, may prefer to be more selective and post only for SHVs that are common in
that State. Having more posting load models to choose from will allow the States to pick the
appropriate load models to obtain more precise posting values. For instance, if a State finds that
seven axle trucks are in common use, but not the five or six axle trucks, then it would be more
advantageous to post for the T7A than the T5A.
4. Having more posting loads would be beneficial to States that show truck symbols with associated
weight limits on posting signs. Here the posting loads are targeted to specific vehicle
configurations.
C-101
CANDIDATE POSTING LOADS (OPTION 1)
T4A
12
8
10’
T5A
12
4’
12.5
8
10’
T6A
11.5
8
8
11.5
10’
17
4’
8
4’
8
4’
4’
17
4’
17
4’
GVW = 62 Kips
17
17
8
4’
GVW = 54 Kips
17
4’
4’
10’
T7A
17
GVW = 69.5 Kips
8
4’
17
4’
Figure C-45 Candidate Posting Loads (Option 1)
C-102
8
4’
8
4’
GVW = 77.5 Kips
CANDIDATE POSTING LOADS (OPTION 2)
T4A
12
8
10’
T5A
12
17
4’
12.5
8
10’
4’
8
4’
GVW = 54 Kips
17
17
4’
17
GVW = 62 Kips
4’
FOR POSTING OF BRIDGES, TRUCK T5A REPRESENTS ALL FORMULA B TRUCK
CONFIGURATIONS (LEGAL TRUCKS) WITH 5 TO 8 AXLES. THE POSTING LOAD
DETERMINED USING T5A WILL APPLY TO ALL FORMULA B TRUCKS WITH 5 TO 8
AXLES.
Figure C-46 Candidate Posting Loads (Option 2)
C-103
TABLE C-49 Moment per Unit Weight -- Simple Spans
Simple Spans
Simple Span Moment Induced per Unit Weight of Truck
Single
Span (Ft)
T4A/Wt
T5A/Wt
T6A/Wt
T7A/Wt
T8/Wt
BFT/Wt
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
1.03
2.00
2.97
3.94
5.07
6.31
7.55
8.80
10.05
11.29
12.54
13.79
15.04
16.29
17.54
18.79
20.04
21.28
22.53
25.03
27.53
30.03
32.53
35.03
37.53
40.03
42.53
45.03
47.53
0.90
1.74
2.71
3.72
4.73
5.80
7.03
8.27
9.51
10.76
12.00
13.25
14.49
15.74
16.98
18.23
19.48
20.73
21.97
24.47
26.97
29.46
31.96
34.46
36.96
39.46
41.96
44.46
46.95
0.80
1.57
2.54
3.58
4.62
5.66
6.91
8.15
9.40
10.65
11.89
13.14
14.39
15.64
16.89
18.14
19.39
20.64
21.88
24.38
26.88
29.39
31.88
34.38
36.88
39.38
41.88
44.38
46.88
0.72
1.40
2.27
3.27
4.33
5.39
6.58
7.83
9.08
10.33
11.58
12.83
14.08
15.33
16.58
17.83
19.08
20.33
21.58
24.08
26.58
29.08
31.58
34.08
36.58
39.08
41.58
44.07
46.58
0.46
0.95
1.71
2.59
3.74
4.89
6.13
7.38
8.63
9.88
11.13
12.38
13.63
14.88
16.13
17.38
18.62
19.87
21.12
23.62
26.12
28.62
31.12
33.62
36.12
38.62
41.12
43.62
46.12
0.70
1.36
2.20
3.16
4.31
5.47
6.72
7.97
9.22
10.47
11.71
12.96
14.21
15.46
16.71
17.96
19.21
20.46
21.71
24.21
26.71
29.21
31.71
34.21
36.71
39.21
41.71
44.20
46.70
C-104
Simple Span Moment Per Unit Weight
14.00
12.00
10.00
T4A/Wt
T5A/Wt
T6A/Wt
T7A/Wt
BFT/Wt
8.00
6.00
4.00
2.00
0.00
10
15
20
25
30
35
40
Figure C-47 Moment Per Unit Weight – Simple Spans
C-105
45
50
55
60
TABLE C-50 Negative Moment per Unit Weight -- Two Span Continuous
Two Span Continuous
Maximum Negative Moment per Unit Weight of Truck
Each
Span (ft)
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
Two Span Continuous MBFT/Wt
T4A/Wt
T5A/Wt
T6A/Wt
T7A/Wt
T8/Wt
-0.50
-0.95
-1.35
-1.75
-2.26
-2.80
-3.15
-3.71
-4.25
-4.78
-5.30
-5.81
-6.33
-6.83
-7.34
-7.84
-8.34
-8.84
-9.33
-10.32
-11.31
-12.29
-13.26
-14.24
-15.21
-16.19
-17.16
-18.13
-19.10
-0.60
-1.23
-1.75
-2.14
-2.46
-2.88
-3.41
-3.94
-4.45
-4.96
-5.47
-5.97
-6.47
-6.97
-7.46
-7.96
-8.45
-8.94
-9.44
-10.41
-11.39
-12.36
-13.34
-14.31
-15.28
-16.25
-17.21
-18.18
-19.15
-0.63
-1.05
-1.60
-2.09
-2.50
-2.84
-3.26
-3.80
-4.32
-4.85
-5.36
-5.87
-6.38
-6.88
-7.38
-7.88
-8.38
-8.87
-9.37
-10.35
-11.33
-12.31
-13.29
-14.26
-15.23
-16.20
-17.17
-18.15
-19.11
-0.56
-0.97
-1.53
-2.03
-2.47
-2.86
-3.21
-3.75
-4.28
-4.80
-5.32
-5.83
-6.34
-6.85
-7.35
-7.85
-8.35
-8.84
-9.34
-10.33
-11.31
-12.29
-13.27
-14.24
-15.22
-16.19
-17.16
-18.13
-19.10
-0.50
-0.88
-1.42
-1.90
-2.39
-2.82
-3.20
-3.63
-4.18
-4.71
-5.23
-5.75
-6.27
-6.78
-7.28
-7.79
-8.29
-8.79
-9.29
-10.28
-11.27
-12.25
-13.23
-14.21
-15.18
-16.16
-17.13
-18.10
-19.07
-0.42
-0.93
-1.44
-1.84
-2.13
-2.48
-3.00
-3.57
-4.12
-4.66
-5.19
-5.72
-6.23
-6.75
-7.26
-7.76
-8.27
-8.77
-9.27
-10.26
-11.25
-12.24
-13.22
-14.20
-15.17
-16.15
-17.12
-18.10
-19.07
C-106
TABLE C-51 Positive Moment per Unit Weight – Two Span Continuous
Two Span Continuous
Maximum Positive Moment Induced Per Unit Weight of Truck
Two Span Continuous M+
Each
Span (ft)
BFT/Wt.
T4A/Wt
T5A/Wt.
T6A/Wt.
T7A/Wt.
T8/Wt
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
0.55
1.09
1.72
2.50
3.36
4.32
5.31
6.32
7.33
8.34
9.36
10.39
11.41
12.44
13.47
14.49
15.52
16.56
17.59
19.65
21.72
23.78
25.85
27.92
29.99
32.06
34.13
36.20
38.28
0.82
1.58
2.37
3.17
4.11
5.09
6.09
7.10
8.12
9.14
10.16
11.19
12.21
13.24
14.27
15.30
16.33
17.36
18.40
20.46
22.53
24.60
26.67
28.74
30.81
32.88
34.95
37.02
39.09
0.71
1.38
2.11
2.93
3.76
4.71
5.69
6.68
7.68
8.69
9.70
10.72
11.74
12.76
13.79
14.81
15.84
16.87
17.90
19.96
22.02
24.09
26.15
28.22
30.29
32.36
34.43
36.50
38.57
0.62
1.25
1.98
2.81
3.66
4.56
5.55
6.54
7.55
8.56
9.57
10.59
11.62
12.64
13.67
14.69
15.72
16.75
17.78
19.85
21.91
23.98
26.04
28.11
30.18
32.25
34.32
36.39
38.46
0.51
1.09
1.77
2.58
3.43
4.28
5.22
6.22
7.22
8.23
9.25
10.27
11.29
12.32
13.34
14.37
15.40
16.43
17.46
19.52
21.58
23.65
25.72
27.79
29.86
31.93
34.00
36.07
38.14
0.35
0.76
1.30
2.02
2.86
3.79
4.78
5.77
6.78
7.79
8.81
9.83
10.85
11.87
12.90
13.93
14.96
15.99
17.02
19.08
21.14
23.21
25.28
27.35
29.41
31.48
33.55
35.63
37.70
C-107
COMPARISON OF RATING FACTORS
To provide a uniform basis that will allow easy comparisons of ratings and postings, the member
resistance for each span in the test suite was assumed such that the span will have a Inventory Rating
Factor = 1.0 (Load Factor Rating) for the current family of three AASHTO legal loads. What this means
is that under LFR ratings these bridges will not have to be load posted for current AASHTO legal loads.
The member resistances thus determined were then used to obtain new Inventory Rating Factors and
posting loads for the proposed BFT truck and the proposed posting vehicles (T4A, T5A, T6A and T7A).
HS20 ratings were also computed for each span. If a bridge rates less than 1.0 for the proposed legal loads
then we have a situation where a bridge that is currently not posted will need to be posted in the future for
the new generation of Formula B trucks. This process is important to understand the potential impact of
the new legal loads on current bridge postings and to also ascertain the practical implications of reducing
the number of new posting vehicles from four to two (i.e., Option 1 vs. Option 2.). Analytical studies
were done on simple spans and continuous bridges with two to four spans (10 ft to 200 ft). Only the
simple span and two-span continuous bridges are discussed here. The findings are similar for the three
and four span bridge configurations.
Live load reactions were computed for transverse members for the proposed rating and posting vehicles.
Transverse member ratings will also be governed by the seven and eight axle trucks. These trucks
produce the highest live load reactions on transverse members.
The following Tables and Figures summarize the results of the analyses:
Rating Factors
Simple Span Rating Factors
Table C-52:
Figure C-48:
Table C-53:
Figure C-49:
Rating Factor – Simple Span Bending
Simple Span Moment Rating Factors
Rating Factor – Simple Span Shear
Simple Span Shear Rating Factors
Two-Span Continuous Rating Factors
Table C-54:
Figure C-50:
Table C-55:
Figure C-51:
Table C-56:
Figure C-52:
Rating Factor – Two Span Continuous Positive Moments
Two Span Continuous +ve Moment Rating Factor
Rating Factor – Two Span Continuous Negative Moments
Two Span Continuous – ve Moment Rating Factor
Rating Factor – Two Span Continuous Shear
Two Span Continuous Shear Rating Factors.
Posting Loads
Simple Span Posting Loads
Table C-57: Posting Load – Simple Span Bending
Figure C-53: Simple Span Moment Posting Load
Table C-58: Posting Load – Simple Span Shear
Figure C-54: Simple Span Shear Posting Load
C-108
Two-Span Continuous Posting Loads
Table C-59:
Figure C-55:
Table C-60:
Figure C-56:
Table C-61:
Figure C-57:
Posting Load – Two Span Continuous Positive Moments
Two Span Continuous +ve Moment Posting Load
Posting Load – Two Span Continuous Negative Moment
Two Span Continuous Negative Moment Posting Load
Posting Load – Two Span Continuous Shear
Two Span Continuous Shear Posting Load
Transverse Member Live Load Reactions
Table C-62: Live Load Reactions on Transverse Floorbeams.
Figure C-58: Reactions per Unit Weight on Transverse members
C-109
TABLE C-52 Rating Factor – Simple Span Bending
RATING FACTOR -- SIMPLE SPAN BENDING
Spans Have an Inv. RF = 1.0 for Current AASHTO Legal Loads
Compares HS20 & AASHTO Legal Trucks With Proposed Rating Truck (BFT) & Posting Loads
Single
Span (ft.)
GOVERNING
AASHTO
LEGAL
MOMENT
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
54.4
95.8
137.7
179.9
225.8
287.7
349.6
411.7
473.9
536.1
618.3
707.1
796.0
885.1
974.3
1063.5
1152.9
1242.3
1343.0
1542.8
1742.5
1942.3
2142.2
2342.0
2541.9
2741.8
2941.7
3141.6
3341.5
GOVERNING Available Live
AASHTO
Load Capacity
LEGAL
= 2.17x LL
TRUCK
Moment
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
118.0
207.9
298.8
390.4
490.0
624.3
758.6
893.4
1028.4
1163.3
1341.7
1534.4
1727.3
1920.7
2114.2
2307.8
2501.8
2695.8
2914.3
3347.9
3781.2
4214.8
4648.6
5082.1
5515.9
5949.7
6383.5
6817.3
7251.1
Rating Factors
Governing
AASHTO
AASHTO
Type 3
Legal Load RF
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.03
1.07
1.10
1.13
1.15
1.17
1.19
1.20
1.22
1.26
1.29
1.32
1.34
1.36
1.38
1.39
1.40
1.41
1.42
T4A
T5A
T6A
T7A
BFT
HS20
0.97
0.89
0.86
0.85
0.83
0.84
0.86
0.87
0.87
0.88
0.91
0.95
0.98
1.01
1.03
1.05
1.07
1.08
1.10
1.14
1.17
1.20
1.22
1.24
1.25
1.27
1.28
1.29
1.30
0.97
0.89
0.82
0.78
0.77
0.80
0.80
0.80
0.80
0.80
0.83
0.86
0.89
0.91
0.93
0.94
0.95
0.97
0.99
1.02
1.04
1.06
1.08
1.10
1.11
1.12
1.13
1.14
1.15
0.97
0.88
0.78
0.72
0.70
0.73
0.73
0.73
0.73
0.72
0.75
0.77
0.80
0.81
0.83
0.84
0.86
0.87
0.88
0.91
0.93
0.95
0.97
0.98
0.99
1.00
1.01
1.02
1.03
0.97
0.88
0.78
0.71
0.67
0.69
0.69
0.68
0.67
0.67
0.69
0.71
0.73
0.75
0.76
0.77
0.78
0.79
0.80
0.83
0.85
0.86
0.88
0.89
0.90
0.91
0.91
0.92
0.93
0.97
0.88
0.78
0.71
0.65
0.66
0.65
0.65
0.64
0.64
0.66
0.68
0.70
0.72
0.73
0.74
0.75
0.76
0.77
0.80
0.82
0.83
0.84
0.86
0.87
0.87
0.88
0.89
0.89
0.68
0.80
0.86
0.87
0.80
0.80
0.78
0.76
0.75
0.75
0.77
0.79
0.81
0.82
0.84
0.85
0.86
0.87
0.88
0.91
0.93
0.94
0.96
0.95
0.92
0.89
0.86
0.84
0.82
C-110
Simple Span Moment Rating Factors
1.60
1.40
Moment Rating Factor
1.20
1.00
AASHTO Type 3
T4A
T5A
T6A
T7A
BFT
HS20
0.80
0.60
0.40
0.20
Span (Ft)
Figure C-48 Simple Span Moment Rating Factors
C-111
200
190
180
170
160
150
140
130
120
110
95
100
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
0.00
TABLE C-53 Rating Factor – Simple Span Shear
RATING FACTOR -- SIMPLE SPAN SHEAR
Spans Have an Inv. RF = 1.0 for Current AASHTO Legal Loads
Compares HS20 & AASHTO Legal Trucks With Proposed Rating Truck (BFT) & Posting Loads
Available Live
Rating Factors
GOVERNING
GOVERNING
Single
AASHTO
Span (ft.) LEGAL SHEAR
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
25.5
28.3
30.1
34.1
36.8
38.7
40.1
41.4
42.1
47.0
49.1
50.8
52.3
54.0
54.8
57.0
56.7
59.5
60.5
62.3
63.7
65.0
66.1
67.0
67.8
68.5
69.2
69.7
70.2
AASHTO
LEGAL
TRUCK
Load
Capacity =
2.17x LL
Shear
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
55.34
61.41
65.32
74.00
79.86
83.98
87.02
89.84
91.36
101.99
106.55
110.24
113.49
117.18
118.92
123.69
123.04
129.12
131.29
135.19
138.23
141.05
143.44
145.39
147.13
148.65
150.16
151.25
152.33
Governing
AASHTO
Legal Load
RF
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
AASHTO Type
3
T4A
T5A
T6A
T7A
BFT
HS20
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.10
1.13
1.16
1.18
1.21
1.22
1.26
1.24
1.30
1.32
1.34
1.36
1.39
1.40
1.41
1.43
1.44
1.45
1.46
1.46
0.96
0.89
0.85
0.87
0.89
0.89
0.90
0.91
0.91
1.00
1.03
1.05
1.08
1.10
1.11
1.15
1.14
1.19
1.20
1.23
1.25
1.27
1.29
1.30
1.31
1.32
1.33
1.34
1.35
0.96
0.85
0.81
0.83
0.83
0.82
0.82
0.82
0.82
0.90
0.92
0.94
0.96
0.98
0.99
1.02
1.01
1.05
1.07
1.09
1.11
1.12
1.13
1.15
1.16
1.16
1.17
1.18
1.18
0.96
0.85
0.81
0.83
0.83
0.81
0.79
0.79
0.78
0.84
0.86
0.88
0.89
0.91
0.91
0.94
0.93
0.97
0.98
1.00
1.01
1.02
1.03
1.04
1.05
1.05
1.06
1.06
1.07
0.96
0.85
0.81
0.83
0.83
0.81
0.78
0.76
0.74
0.80
0.82
0.83
0.84
0.85
0.85
0.87
0.86
0.89
0.90
0.92
0.93
0.94
0.94
0.95
0.95
0.96
0.97
0.97
0.97
0.96
0.85
0.78
0.80
0.81
0.80
0.77
0.76
0.74
0.79
0.81
0.81
0.82
0.83
0.83
0.86
0.84
0.88
0.88
0.90
0.90
0.91
0.92
0.93
0.93
0.93
0.94
0.94
0.94
0.84
0.88
0.75
0.76
0.76
0.75
0.74
0.74
0.73
0.80
0.82
0.83
0.84
0.86
0.87
0.89
0.88
0.92
0.93
0.95
0.96
0.98
0.99
1.00
0.98
0.95
0.92
0.88
0.86
C-112
Simple Span Shear Rating Factors
1.60
1.40
Shear Rating Factor
1.20
1.00
AASHTO Type 3
T4A
T5A
T6A
T7A
BFT
HS20
0.80
0.60
0.40
0.20
Span (Ft.)
Figure C-49 Simple Span Shear Rating Factors
C-113
200
190
180
170
160
150
140
130
120
110
100
95
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
0.00
TABLE C-54 Rating Factor – Two Span Continuous Positive Moments
RATING FACTOR -- TWO-SPAN CONTINUOUS POSITIVE MOMENT
Spans Have an Inv. RF = 1.0 for Current AASHTO Legal Loads
Each
Span (ft.)
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
Available
Live Load
Governing
Capacity =
AASHTO
2.17x LL
Legal Load
Shear
RF
AASHTO
legal Pos
Moment
GOVERNING
AASHTO
LEGAL
TRUCK
44.1
Type 3
95.7
77.2
111.5
146.2
185.5
233.3
282.2
331.9
382.0
432.5
491.4
560.9
631.2
702.2
773.6
845.4
917.6
990.1
1062.8
1214.0
1376.1
1539.0
1702.2
1865.9
2029.9
2194.1
2358.5
2523.1
2687.8
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
167.5
242.0
317.3
402.5
506.3
612.4
720.2
828.9
938.5
1066.3
1217.2
1369.7
1523.8
1678.7
1834.5
1991.2
2148.5
2306.3
2634.4
2986.1
3339.6
3693.8
4049.0
4404.9
4761.2
5117.9
5475.1
5832.5
Rating Factor - Positive Moment
AASHTO
Type 3
T4A
T5A
T6A
T7A
BFT
HS20
1.00
1.00
1.00
1.00
1.02
1.11
1.00
0.67
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.02
1.05
1.08
1.10
1.12
1.14
1.16
1.18
1.19
1.22
1.25
1.28
1.30
1.32
1.34
1.36
1.37
1.38
1.39
0.90
0.87
0.85
0.84
0.85
0.86
0.87
0.87
0.88
0.90
0.93
0.96
0.98
1.00
1.02
1.04
1.06
1.07
1.10
1.13
1.16
1.18
1.20
1.22
1.24
1.25
1.26
1.27
0.90
0.85
0.81
0.80
0.80
0.80
0.80
0.80
0.80
0.82
0.84
0.87
0.89
0.91
0.92
0.93
0.95
0.96
0.98
1.01
1.03
1.05
1.07
1.08
1.09
1.10
1.11
1.12
0.89
0.81
0.75
0.73
0.74
0.73
0.73
0.73
0.73
0.74
0.76
0.78
0.80
0.81
0.83
0.84
0.85
0.86
0.88
0.90
0.92
0.94
0.95
0.97
0.98
0.99
1.00
1.01
0.91
0.81
0.73
0.70
0.70
0.70
0.69
0.68
0.68
0.69
0.70
0.72
0.74
0.75
0.76
0.77
0.78
0.79
0.80
0.82
0.84
0.85
0.87
0.88
0.89
0.90
0.90
0.91
0.89
0.81
0.73
0.69
0.68
0.66
0.66
0.65
0.65
0.66
0.68
0.69
0.71
0.72
0.73
0.74
0.75
0.76
0.77
0.79
0.81
0.82
0.84
0.85
0.86
0.86
0.87
0.88
0.78
0.84
0.85
0.81
0.81
0.79
0.77
0.76
0.75
0.76
0.78
0.80
0.81
0.82
0.84
0.85
0.85
0.86
0.88
0.90
0.92
0.93
0.95
0.94
0.92
0.89
0.87
0.85
C-114
Two Span Continuous +ve Moment RF
1.60
1.40
1.20
Rating Factor
1.00
AASHTO Type 3
T4A
T5A
T6A
T7A
BFT
HS20
0.80
0.60
0.40
0.20
Each Span (Ft)
Figure C-50 Two Span Continuous +ve Moment Rating Factor
C-115
200
190
180
170
160
150
140
130
120
110
100
95
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
0.00
TABLE C-55 Rating Factor – Two Span Continuous Negative Moments
RATING FACTOR -- TWO SPAN CONTINUOUS NEGATIVE MOMENTS
Spans Have an Inv. RF = 1.0 for Current AASHTO Legal Loads
Each
Span (ft.)
AASHTO
legal Neg
Moment
GOVERNING
AASHTO
LEGAL
TRUCK
Available
Live Load
Capacity =
2.17x LL
Moment
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
-29.5
-63.5
-93.3
-139.6
-186.7
-225.1
-256.1
-283.0
-315.4
-343.2
-367.3
-388.3
-406.9
-427.4
-469.6
-515.8
-561.2
-606.0
-650.3
-737.4
-823.0
-907.4
-990.7
-1073.3
-1155.2
-1236.5
-1317.4
-1397.9
-1478.0
Type 3
Type 3
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
-64.0
-137.8
-202.5
-302.9
-405.1
-488.5
-555.7
-614.1
-684.4
-744.7
-797.0
-842.6
-883.0
-927.5
-1019.0
-1119.3
-1217.8
-1315.0
-1411.2
-1600.2
-1785.9
-1969.1
-2149.8
-2329.1
-2506.8
-2683.2
-2858.8
-3033.4
-3207.3
Rating Factors - Negative moment
Governing
AASHTO
Legal Load
RF
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
AASHTO
Type 3
T4A
T5A
T6A
T7A
BFT
HS20
1.00
1.00
1.00
1.22
1.44
1.58
1.59
1.51
1.47
1.43
1.38
1.33
1.28
1.25
1.28
1.31
1.34
1.37
1.39
1.43
1.45
1.48
1.49
1.51
1.52
1.53
1.53
1.54
1.55
0.91
0.96
0.99
1.21
1.40
1.45
1.39
1.33
1.31
1.28
1.24
1.20
1.16
1.14
1.16
1.20
1.23
1.25
1.28
1.31
1.34
1.36
1.38
1.39
1.40
1.41
1.42
1.42
1.43
0.76
0.98
0.94
1.08
1.21
1.28
1.27
1.20
1.18
1.14
1.11
1.07
1.03
1.00
1.03
1.06
1.08
1.10
1.12
1.15
1.17
1.19
1.20
1.21
1.22
1.23
1.24
1.24
1.25
0.76
0.95
0.88
0.99
1.09
1.13
1.15
1.09
1.06
1.03
0.99
0.96
0.92
0.90
0.92
0.95
0.97
0.99
1.00
1.03
1.05
1.06
1.07
1.08
1.09
1.10
1.10
1.11
1.11
0.76
0.93
0.85
0.95
1.01
1.03
1.03
1.00
0.97
0.94
0.91
0.87
0.84
0.81
0.83
0.85
0.87
0.89
0.90
0.93
0.94
0.96
0.97
0.97
0.98
0.99
0.99
1.00
1.00
0.74
0.84
0.86
1.00
1.03
1.01
1.02
0.95
0.93
0.90
0.87
0.83
0.80
0.78
0.80
0.82
0.84
0.86
0.87
0.89
0.91
0.92
0.93
0.94
0.95
0.95
0.96
0.96
0.97
0.69
0.71
0.76
0.89
0.97
0.98
0.96
0.89
0.85
0.80
0.74
0.69
0.64
0.60
0.60
0.59
0.59
0.58
0.57
0.55
0.53
0.51
0.49
0.47
0.45
0.43
0.41
0.40
0.38
C-116
Two Span Continuous -ve Moment RF
1.80
1.60
1.40
Rating Factor
1.20
AASHTO Type 3
T4A
T5A
T6A
T7A
BFT
HS20
1.00
0.80
0.60
0.40
0.20
0.00
Each Span (Ft)
Figure C-51 Two Span Continuous – ve Moment Rating Factor
C-117
TABLE C-56 Rating Factor – Two Span Continuous Shear
RATING FACTOR -- TWO SPAN CONTINUOUS SHEAR
Spans Have an Inv. RF = 1.0 for Current AASHTO Legal Loads
GOVERNING GOVERNING Available Live
Each
AASHTO
AASHTO
Load Capacity Governing
AASHTO
Span (ft.)
LEGAL
LEGAL
= 2.17x LL
Legal Load
Shear
TRUCK
Shear
RF
10
27.5
Type 3
59.7
1.00
15
30.3
Type 3
65.8
1.00
20
31.3
Type 3
67.9
1.00
25
36.3
Type 3
78.8
1.00
30
39.1
Type 3
84.8
1.00
35
41.1
Type 3
89.2
1.00
40
42.5
Type 3-S2
92.2
1.00
45
44.8
Type 3-S2
97.2
1.00
50
48.3
Type 3-S2
104.8
1.00
55
51.0
Type 3-S2
110.7
1.00
60
53.3
Type 3-S2
115.7
1.00
65
55.1
Type 3-S2
119.6
1.00
70
56.8
Type 3-S2
123.3
1.00
75
58.8
Type 3-3
127.6
1.00
80
60.5
Type 3-3
131.3
1.00
85
61.9
Type 3-3
134.3
1.00
90
63.2
Type 3-3
137.1
1.00
95
64.3
Type 3-3
139.5
1.00
100
65.3
Type 3-3
141.7
1.00
110
67.0
Type 3-3
145.4
1.00
120
68.4
Type 3-3
148.4
1.00
130
69.5
Type 3-3
150.8
1.00
140
70.4
Type 3-3
152.8
1.00
150
71.2
Type 3-3
154.5
1.00
160
71.9
Type 3-3
156.0
1.00
170
72.4
Type 3-3
157.1
1.00
180
73.0
Type 3-3
158.4
1.00
190
73.4
Type 3-3
159.3
1.00
200
73.8
Type 3-3
160.1
1.00
Shear Rating Factors
AASHTO
Type 3
T4A
T5A
T6A
T7A
BFT
HS20
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.03
1.09
1.13
1.17
1.20
1.23
1.26
1.29
1.32
1.34
1.36
1.37
1.40
1.43
1.44
1.46
1.47
1.48
1.49
1.50
1.50
1.51
0.95
0.88
0.83
0.87
0.88
0.89
0.90
0.93
0.99
1.03
1.07
1.10
1.12
1.16
1.18
1.21
1.23
1.25
1.26
1.29
1.31
1.33
1.34
1.35
1.36
1.37
1.38
1.39
1.39
0.95
0.84
0.78
0.82
0.82
0.82
0.81
0.84
0.88
0.92
0.95
0.97
0.99
1.02
1.05
1.07
1.08
1.10
1.11
1.13
1.15
1.17
1.18
1.19
1.20
1.20
1.21
1.21
1.22
0.91
0.83
0.77
0.81
0.81
0.79
0.77
0.79
0.83
0.85
0.88
0.89
0.91
0.94
0.96
0.97
0.98
1.00
1.01
1.03
1.04
1.05
1.06
1.07
1.08
1.08
1.09
1.09
1.09
0.91
0.81
0.75
0.80
0.80
0.78
0.75
0.75
0.78
0.80
0.82
0.83
0.84
0.86
0.88
0.89
0.90
0.91
0.92
0.94
0.95
0.96
0.96
0.97
0.98
0.98
0.98
0.99
0.99
0.91
0.80
0.72
0.76
0.77
0.76
0.74
0.74
0.77
0.79
0.80
0.81
0.83
0.84
0.86
0.87
0.88
0.89
0.90
0.91
0.92
0.93
0.94
0.94
0.95
0.95
0.96
0.96
0.96
0.86
0.87
0.71
0.73
0.74
0.73
0.72
0.74
0.78
0.81
0.83
0.85
0.87
0.89
0.91
0.93
0.94
0.95
0.96
0.96
0.93
0.89
0.86
0.83
0.80
0.77
0.75
0.72
0.70
C-118
Two Span Continuous Shear Rating Factors
1.60
1.40
1.20
Rating Factor
1.00
AASHTO Type 3
T4A
T5A
T6A
T7A
BFT
HS20
0.80
0.60
0.40
0.20
Each Span (Ft)
Figure C-52 Two Span Continuous Shear Rating Factors
C-119
200
190
180
170
160
150
140
130
120
110
100
95
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
0.00
TABLE C-57 Posting Load – Simple Span Bending
POSTING LOADS -- SIMPLE SPAN BENDING
Spans Have an Inv. RF = 1.0 for Current AASHTO Legal Loads
Compares HS20 & AASHTO Legal Trucks With Proposed Rating Truck (BFT) & Posting Loads
Posting Load in Tons
GOVERNING
Single
AASHTO
Span (ft.)
LEGAL
TRUCK
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Governing
AASHTO
Legal Load RF
AASHTO
Type 3
T4A
T5A
T6A
T7A
BFT
HS20
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
25.0
25.0
25.0
25.0
25.0
25.0
25.0
25.0
25.0
25.0
25.8
26.8
27.5
28.2
28.7
29.2
29.6
30.0
30.6
31.6
32.3
33.0
33.5
34.0
34.4
34.8
35.1
35.3
35.6
26.3
24.0
23.2
22.8
22.3
22.8
23.1
23.4
23.6
23.7
24.6
25.6
26.5
27.2
27.8
28.3
28.8
29.2
29.8
30.8
31.6
32.3
32.9
33.4
33.9
34.2
34.6
34.9
35.2
30.2
27.5
25.4
24.2
23.9
24.8
24.9
24.9
24.9
24.9
25.8
26.7
27.5
28.1
28.7
29.2
29.6
30.0
30.6
31.5
32.3
33.0
33.5
34.0
34.4
34.7
35.1
35.3
35.6
33.9
30.6
27.2
25.1
24.4
25.4
25.3
25.2
25.2
25.2
26.0
26.9
27.7
28.3
28.8
29.3
29.7
30.1
30.7
31.6
32.4
33.0
33.6
34.1
34.5
34.8
35.1
35.4
35.6
37.78
34.12
30.28
27.54
26.10
26.71
26.56
26.29
26.10
25.95
26.70
27.56
28.27
28.87
29.39
29.83
30.22
30.56
31.12
32.04
32.78
33.40
33.92
34.36
34.75
35.08
35.38
35.64
35.87
39.0
35.2
31.3
28.4
26.2
26.3
26.0
25.8
25.7
25.6
26.4
27.3
28.0
28.6
29.2
29.6
30.0
30.4
30.9
31.9
32.6
33.3
33.8
34.2
34.6
35.0
35.3
35.5
35.8
24.48
28.74
30.98
31.23
28.82
28.68
27.98
27.51
27.17
26.91
27.60
28.41
29.07
29.64
30.11
30.52
30.87
31.19
31.73
32.60
33.31
33.89
34.39
34.07
33.06
32.08
31.13
30.22
29.34
C-120
Simple Span Moment Posting Loads
40.0
38.0
36.0
Posting Load (Tons)
34.0
AASHTO Type 3
T4A
T5A
T6A
T7A
BFT
32.0
30.0
28.0
26.0
24.0
22.0
Span (Ft)
Figure C-53 Simple Span Moment Posting Load
C-121
200
190
180
170
160
150
140
130
120
110
100
95
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
20.0
TABLE C-58 Posting Load – Simple Span Shear
POSTING LOADS -- SIMPLE SPAN SHEAR
Spans Have an Inv. RF = 1.0 for Current AASHTO Legal Loads
Compares HS20 & AASHTO Legal Trucks With Proposed Rating Truck (BFT) & Posting Loads
Posting Load in Tons
GOVERNING
Single
AASHTO
Span (ft.)
LEGAL
TRUCK
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Governing
AASHTO
Legal Load
RF
AASHTO Type
3
T4A
T5A
T6A
T7A
BFT
HS20
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
25.0
25.0
25.0
25.0
25.0
25.0
25.0
25.1
25.0
27.5
28.3
28.9
29.5
30.2
30.4
31.5
31.1
32.5
32.9
33.6
34.1
34.6
35.0
35.3
35.7
35.9
36.2
36.4
36.6
25.8
24.0
23.0
23.6
23.9
24.1
24.3
24.5
24.4
26.9
27.7
28.5
29.1
29.8
30.0
31.0
30.7
32.1
32.5
33.2
33.8
34.3
34.8
35.1
35.4
35.7
36.0
36.2
36.4
29.6
26.5
25.0
25.7
25.6
25.5
25.4
25.5
25.3
27.8
28.6
29.2
29.7
30.4
30.6
31.7
31.3
32.6
33.0
33.8
34.3
34.7
35.1
35.5
35.8
36.1
36.3
36.5
36.6
33.2
29.7
28.0
28.9
28.8
28.2
27.6
27.4
26.9
29.3
30.0
30.5
31.0
31.6
31.7
32.7
32.3
33.6
34.0
34.6
35.0
35.5
35.8
36.2
36.4
36.6
36.8
37.0
37.1
37.0
33.1
31.3
32.2
32.1
31.4
30.2
29.5
28.8
31.1
31.7
32.1
32.4
32.9
32.9
33.9
33.3
34.7
34.9
35.5
35.9
36.2
36.6
36.8
37.0
37.2
37.4
37.5
37.6
38.2
34.2
31.0
32.0
32.5
31.9
31.0
30.3
29.5
31.8
32.2
32.6
32.8
33.4
33.4
34.3
33.7
35.0
35.3
35.8
36.1
36.5
36.8
37.0
37.3
37.4
37.6
37.7
37.8
30.20
31.84
27.09
27.40
27.37
26.90
26.59
26.47
26.22
28.63
29.36
29.93
30.42
31.05
31.22
32.21
31.84
33.21
33.56
34.19
34.69
35.14
35.57
35.84
35.32
34.11
32.95
31.84
30.82
C-122
Simple Span Shear Posting Loads
40.0
38.0
36.0
Posting Load (Tons)
34.0
AASHTO Type 3
T4A
T5A
T6A
T7A
BFT
32.0
30.0
28.0
26.0
24.0
22.0
Span (Ft)
Figure C-54 Simple Span Shear Posting Load
C-123
200
190
180
170
160
150
140
130
120
110
100
95
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
20.0
TABLE C-59 Posting Load – Two Span Continuous Positive Moments
POSTING LOADS -- TWO SPAN CONTINUOUS POSITIVE MOMENTS
Spans Have an Inv. RF = 1.0 for Current AASHTO Legal Loads
GOVERNING Governing
Each
AASHTO
AASHTO
Span (ft.)
LEGAL
Legal Load
TRUCK
RF
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
Posting Load in Tons
AASHTO
Type 3
T4A
T5A
T6A
T7A
BFT
HS20
Type 3
1.00
25.00
27.0
31.0
35.5
42.8
40.0
24.1
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
25.00
25.00
25.00
25.00
25.00
25.00
25.00
25.00
25.00
25.42
26.25
26.97
27.58
28.12
28.60
29.02
29.40
29.74
30.46
31.29
31.99
32.58
33.09
33.54
33.93
34.28
34.59
34.87
24.4
23.5
23.1
22.6
22.9
23.2
23.4
23.5
23.7
24.2
25.1
25.8
26.5
27.1
27.6
28.1
28.5
28.9
29.7
30.5
31.3
31.9
32.5
32.9
33.4
33.7
34.1
34.4
28.0
26.4
25.0
24.7
24.8
24.8
24.8
24.9
24.9
25.3
26.2
26.9
27.5
28.1
28.5
29.0
29.3
29.7
30.4
31.2
31.9
32.5
33.1
33.5
33.9
34.3
34.6
34.8
30.8
28.2
26.0
25.3
25.6
25.4
25.4
25.3
25.3
25.7
26.5
27.2
27.8
28.3
28.8
29.2
29.6
29.9
30.6
31.4
32.1
32.7
33.2
33.6
34.0
34.4
34.7
34.9
35.4
31.5
28.3
27.1
27.2
27.0
26.7
26.4
26.3
26.6
27.3
28.0
28.5
29.0
29.4
29.8
30.1
30.4
31.1
31.9
32.5
33.1
33.6
34.0
34.4
34.7
35.0
35.2
35.5
32.4
29.2
27.6
27.0
26.6
26.3
26.1
25.9
26.2
27.0
27.7
28.2
28.7
29.2
29.6
29.9
30.2
30.9
31.7
32.4
32.9
33.4
33.8
34.2
34.5
34.8
35.1
28.1
30.4
30.5
29.1
29.1
28.3
27.8
27.5
27.2
27.4
28.1
28.7
29.2
29.7
30.1
30.4
30.7
31.0
31.7
32.4
33.1
33.6
34.1
33.9
33.0
32.1
31.3
30.4
C-124
Two Span Continuous +ve Moment Posting Load
45.0
Posting Load (Tons)
40.0
AASHTO Type 3
T4A
T5A
T6A
T7A
BFT
35.0
30.0
25.0
Figure C-55 Two Span Continuous +ve Moment Posting Load
C-125
200
190
180
170
160
150
140
130
120
110
95
Each Span (Ft)
100
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
20.0
TABLE C-60 Posting Load – Two Span Continuous Negative Moment
POSTING LOAD -- TWO SPAN CONTINUOUS NEGATIVE MOMENT
Spans Have an Inv. RF = 1.0 for Current AASHTO Legal Loads
GOVERNING
Each
AASHTO
Span (ft.)
LEGAL
TRUCK
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
Type 3
Type 3
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Posting Load in Tons
Governing
AASHTO
Legal Load
RF
AASHTO
Type 3
T4A
T5A
T6A
T7A
BFT
HS20
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
25.0
25.0
25.0
30.5
35.9
39.5
39.8
37.7
36.8
35.7
34.5
33.2
32.0
31.2
31.9
32.8
33.6
34.2
34.8
35.7
36.4
36.9
37.3
37.7
37.9
38.2
38.4
38.5
38.7
24.7
25.8
26.6
32.5
37.9
39.1
37.5
36.0
35.4
34.6
33.6
32.5
31.4
30.7
31.5
32.4
33.2
33.9
34.5
35.4
36.1
36.7
37.1
37.5
37.8
38.1
38.3
38.4
38.6
23.4
30.3
29.2
33.3
37.4
39.7
39.3
37.3
36.5
35.4
34.3
33.1
31.9
31.1
31.8
32.7
33.5
34.2
34.7
35.6
36.3
36.9
37.3
37.6
37.9
38.2
38.4
38.5
38.7
26.3
32.9
30.5
34.5
37.8
39.4
39.9
37.8
36.9
35.7
34.5
33.3
32.1
31.2
31.9
32.9
33.6
34.3
34.8
35.7
36.4
36.9
37.3
37.7
38.0
38.2
38.4
38.6
38.7
29.3
36.0
32.8
36.7
39.1
40.0
40.0
38.9
37.8
36.4
35.1
33.7
32.5
31.5
32.2
33.1
33.8
34.5
35.0
35.9
36.5
37.0
37.4
37.8
38.0
38.3
38.5
38.6
38.7
29.6
33.4
34.6
40.0
41.3
40.2
40.6
38.2
37.1
35.9
34.7
33.4
32.2
31.3
32.0
32.9
33.7
34.3
34.8
35.7
36.4
36.9
37.3
37.7
38.0
38.2
38.4
38.6
38.7
24.9
25.5
27.3
32.2
34.9
35.4
34.7
32.2
30.5
28.7
26.8
24.9
23.2
21.8
21.5
21.4
21.2
20.9
20.5
19.8
19.0
18.2
17.5
16.8
16.1
15.4
14.8
14.3
13.8
C-126
Two Span Continuous -ve Moment Posting Loads
45.0
Posting Load (Tons)
40.0
AASHTO Type 3
T4A
T5A
T6A
T7A
BFT
35.0
30.0
25.0
Each Span (Ft)
Figure C-56 Two Span Continuous Negative Moment Posting Load
C-127
200
190
180
170
160
150
140
130
120
110
95
100
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
20.0
TABLE C-61 Posting Load – Two Span Continuous Shear
POSTING LOADS -- TWO SPAN CONTINUOUS SHEAR
Spans Have an Inv. RF = 1.0 for Current AASHTO Legal Loads
Each
Span (ft.)
GOVERNING
AASHTO
LEGAL
TRUCK
Governing
AASHTO
Legal Load
RF
AASHTO
Type 3
T4A
T5A
T6A
T7A
BFT
HS20
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-S2
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
Type 3-3
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
25.0
25.0
25.0
25.0
25.0
25.0
25.0
25.7
27.3
28.3
29.3
30.0
30.7
31.5
32.3
32.9
33.5
33.9
34.3
35.0
35.6
36.0
36.4
36.7
37.0
37.2
37.4
37.6
37.7
25.6
23.9
22.4
23.4
23.8
24.1
24.3
25.0
26.7
27.8
28.8
29.6
30.3
31.2
32.0
32.6
33.1
33.6
34.0
34.8
35.4
35.9
36.2
36.5
36.8
37.0
37.3
37.5
37.6
29.4
26.2
24.1
25.5
25.3
25.3
25.2
25.9
27.4
28.5
29.5
30.1
30.8
31.7
32.4
33.0
33.5
34.0
34.4
35.1
35.7
36.1
36.5
36.8
37.1
37.2
37.5
37.6
37.8
31.6
28.8
26.7
28.3
28.0
27.4
26.9
27.3
28.7
29.7
30.5
31.1
31.7
32.5
33.2
33.7
34.2
34.6
35.0
35.7
36.2
36.6
36.9
37.2
37.4
37.6
37.8
38.0
38.0
35.3
31.5
28.9
31.0
31.0
30.1
29.0
29.1
30.2
31.0
31.7
32.2
32.7
33.5
34.1
34.6
35.0
35.3
35.7
36.3
36.7
37.1
37.4
37.6
37.8
38.0
38.1
38.3
38.4
36.4
32.1
28.6
30.4
30.8
30.2
29.6
29.6
30.7
31.4
32.1
32.5
33.0
33.7
34.3
34.8
35.2
35.6
35.9
36.5
36.9
37.2
37.5
37.7
37.9
38.1
38.3
38.3
38.5
30.9
31.3
25.4
26.3
26.6
26.3
26.1
26.6
28.0
29.1
29.9
30.6
31.2
32.1
32.8
33.4
33.9
34.3
34.7
34.5
33.3
32.1
30.9
29.8
28.8
27.8
26.8
25.9
25.1
Posting Load in Tons
C-128
Two Span Continuous Shear Posting Loads
40.0
38.0
36.0
Posting Load (Tons)
34.0
32.0
AASHTO Type 3
T4A
T5A
T6A
T7A
BFT
30.0
28.0
26.0
24.0
22.0
20.0
Each Span (Ft)
Figure C-57 Two Span Continuous Shear Posting Load
C-129
TABLE C-62 Live Load Reactions on Transverse Floorbeams.
LIVE LOAD REACTIONS (R) IN KIPS PER WHEEL LINE ON TRANSVERSE FLOORBEAMS (No Impact)
TYPE OF LOADING
STRINGER
SPAN (FT)
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
TYPE 3 TYPE 3S2 TYPE 3-3
13.6
13.9
14.2
14.4
14.6
14.8
15.3
15.8
16.4
16.8
17.2
17.6
18.0
18.3
18.5
18.8
19.0
19.3
19.5
19.7
19.9
12.4
12.7
13.1
13.7
14.2
14.6
15.0
15.4
15.6
15.9
16.1
16.3
16.5
16.7
16.9
17.0
17.5
18.2
18.8
19.4
20.1
11.2
11.5
11.7
11.9
12.0
12.2
12.3
12.7
13.3
13.7
14.2
14.5
14.9
15.2
15.5
15.7
16.2
16.8
17.5
18.0
18.8
Governing
AASHTO
Legal
HS-20
T4A
T5A
T6A
T7A
BFT
13.6
13.9
14.2
14.4
14.6
14.8
15.3
15.8
16.4
16.8
17.2
17.6
18.0
18.3
18.5
18.8
19.0
19.3
19.5
19.7
20.1
16.0
16.0
16.0
16.0
16.0
17.3
18.5
19.5
20.4
21.3
22.0
22.7
23.3
23.8
24.3
24.8
25.2
25.6
26.0
26.3
26.7
16.0
16.5
16.8
17.2
17.4
18.1
18.6
19.1
19.6
19.9
20.3
20.6
20.9
21.2
21.4
21.6
21.8
22.0
22.2
22.4
22.5
16.8
17.5
18.2
18.7
19.1
19.5
19.9
20.2
20.4
21.0
21.5
22.0
22.4
22.7
23.1
23.4
23.7
24.0
24.2
24.4
24.7
17.6
18.6
19.5
20.2
20.9
21.4
21.9
22.3
22.7
23.3
23.9
24.4
24.9
25.3
25.7
26.1
26.4
26.7
27.0
27.3
27.5
17.6
18.6
19.5
20.5
21.4
22.2
22.9
23.5
24.0
24.8
25.5
26.1
26.7
27.2
27.7
28.1
28.5
28.9
29.3
29.6
29.9
17.6
18.6
19.5
20.2
20.9
21.4
21.9
22.3
23.0
23.7
24.3
24.8
25.3
26.0
26.6
27.1
27.6
28.1
28.5
28.9
29.3
C-130
Ratio =
Governing
FBF/AASHTO
FBF
LEGAL
17.6
18.6
19.5
20.5
21.4
22.2
22.9
23.5
24.0
24.8
25.5
26.1
26.7
27.2
27.7
28.1
28.5
28.9
29.3
29.6
29.9
1.29
1.34
1.37
1.42
1.47
1.50
1.50
1.49
1.46
1.48
1.48
1.48
1.48
1.49
1.50
1.49
1.50
1.50
1.50
1.50
1.49
Ratio =
Governing
FBF/Truck
BFT
1.00
1.00
1.00
1.01
1.02
1.04
1.05
1.05
1.04
1.05
1.05
1.05
1.06
1.05
1.04
1.04
1.03
1.03
1.03
1.02
1.02
Reactions Per Unit Weight on Transverse Members
0.90
0.80
0.70
Reaction (K)
0.60
T4A
0.50
T5A
T6A
T7A
0.40
BFT
0.30
0.20
0.10
0.00
10
11
12
13
14
15
16
17
18
19
20
21
22
Stringer Span (Ft)
Figure C-58 Reactions per Unit Weight on Transverse members
C-131
23
24
25
26
27
28
29
30
SUMMARY OF FINDINGS
The member resistance for each span in the test suite was assumed such that the span will have a Rating
Factor = 1.0 for the current family of three AASHTO legal loads. The tables and figures also show the
single unit AASHTO Type 3 rating factors, which may be greater than 1.0 for spans governed by the
AASHTO combination vehicles. In all cases the Type 3 truck has the highest rating factors.
The results of the analyses provide a detailed assessment of the performance of existing bridges under the
new loadings and potential impacts on current ratings and postings.
Rating Factors – Longitudinal Members
A) Moment Rating Factors – Simple Spans
 Truck BFT will have the lowest ratings, varies from 0.97 to 0.64 (Table C-52). This indicates
that all spans should be subjected to a posting analysis for the new posting vehicles.
 Spans over 110 ft will have a RF > 1.0 for T5A, whereas, T6A, T7A and BFT will have a RF
< 1.0 for these spans (Fig C-48). If T5A was to be used as a single posting loads for all
vehicles with 5 to 8 axles, we could have a situation (say a 140 ft span) where T5A is used for
posting a bridge even though the bridge has adequate rating for T5A. Though it is a valid
analytical convenience as shown in the previous QPR, there is some concern that this may
cause confusion in the mind of the evaluator.
 The moment ratings for the 7 and 8 axle BFT trucks are lower than the HS20 ratings for most
spans (Fig.C-48). This shows that HS20 is not a suitable screening load model for all Formula
B trucks.
B) Shear Rating Factors – Simple Spans
 Truck BFT will have the lowest ratings, varies from 0.96 to 0.74 (Table C-53). This indicates
that all spans should be subjected to a posting analysis for the new posting vehicles.
 Spans over 85 ft will have a RF > 1.0 for T5A, whereas, T6A (spans up to 120’), T7A and
BFT will have a RF < 1.0 for these spans (Fig C-49). Same concerns about using T5A for
posting a bridge even though the bridge has adequate rating for T5A applies here as well.
 The shear ratings for the 7 and 8 axle BFT trucks are lower than the HS20 ratings for most
spans (Fig. C-49). HS20 is not a suitable screening load model for all Formula B trucks.
C) Moment Rating Factors -- Two Span Continuous Positive Moment
 Truck BFT will have the lowest ratings, varies from 1.0 to 0.68 (Table C-54). This indicates
that all spans over 10 ft should be subjected to a posting analysis for the new posting
vehicles.
 Spans over 110 ft will have a RF > 1.0 for T5A, whereas, T6A, T7A and BFT will have a RF
< 1.0 for these spans (Fig C-50). Same concerns about using T5A for posting a bridge even
though the bridge has adequate rating for T5A applies here as well for spans over 110 ft.
 The ratings for the 7 and 8 axle BFT trucks are lower than the HS20 ratings for most spans
(Fig. C-50). HS20 is not a suitable screening load model for all Formula B trucks.
C-132
D) Moment Rating Factors -- Two span Continuous Negative Moment
 Truck BFT will have the lowest ratings, varies from 1.02 to 0.74 (Table C-55). This indicates
that most spans will require a posting analysis for the new posting vehicles.
 Spans over 20 ft will have a RF > 1.0 for T5A, whereas, T7A and BFT will have a RF < 1.0
for most spans (Fig C-51). Same concerns about using T5A for posting a bridge even though
the bridge has adequate rating for T5A applies here as well.
 HS20 negative moment ratings are lower than the BFT ratings for all spans (Fig. C-51). HS20
rating factors for the longer spans (governed by the lane load model) are significantly lower
than the BFT ratings.
E) Shear Rating Factors -- Two span Continuous
 Truck BFT will have the lowest ratings, varies from 0.96 to 0.72 (Table C-56). This indicates
that all spans will require a posting analysis for shear for the new posting vehicles.
 Spans over 70 ft will have a RF > 1.0 for T5A, whereas, T7A and BFT will have a RF < 1.0
for all spans (Fig C-52). Using T5A as a posting load even though a span has adequate rating
for T5A has to be considered.
 HS20 shear moment ratings are lower than the BFT shear ratings for the longer spans
governed by the lane load model (Fig C-52).
Posting Loads – Longitudinal Members
A) Posting Loads – Simple Span Bending
 T4A will produce the lowest posting load of all Formula B vehicles (Table C-57). This
compact truck has the highest moment per unit weight resulting in the lowest posting limit.
 Of the trucks with 5 or more axles, T5A will have the lowest posting load (Fig C-53).
However, the degree of conservatism introduced by using T5A as a single posting load is
dependant on the span length. An adverse impact is seen in the very short spans that are
controlled by wheel loads (see table below).
TABLE C-63 Posting Loads (Tons) – Simple Span Bending
Span length
20 Ft
40 Ft
80 Ft
120 Ft
T5A Posting Load
25.4
24.9
28.7
32.3
(Tons)
T6A Posting Load
27.2
25.3
28.8
32.4
(Tons)
T7A Posting Load
30.3
26.6
29.4
32.8
(Tons)
B) Posting Loads – Simple Span Shear
 T4A will produce the lowest posting load of all Formula B vehicles (Table C-58).
 Of the trucks with 5 or more axles, T5A will have the lowest posting load (Fig C-54).
However, the degree of conservatism introduced by using T5A as a single posting load is
C-133
dependant on the span length. An adverse impact is seen in the very short spans that are
controlled by wheel loads (see table below).
TABLE C-64 Posting Loads (Tons) – Simple Span Shear
Span length
20 Ft
40 Ft
80 Ft
120 Ft
T5A Posting Load
26.4
24.8
28.1
31.2
(Tons)
T6A Posting Load
28.2
25.4
28.3
31.4
(Tons)
T7A Posting Load
31.5
27.0
29.0
31.9
(Tons)
C) Posting Loads – Two Span Continuous Positive Moments
 T4A will produce the lowest posting load of all Formula B vehicles (Table C-59). This
compact truck has the highest moment per unit weight resulting in the lowest posting limit.
 Of the trucks with 5 or more axles, T5A will have the lowest posting load (Fig C-55).
However, the degree of conservatism introduced by using T5A as a single posting load is
dependant on the span length. An adverse impact is seen in the very short spans that are
controlled by wheel loads (see table below).
TABLE C-65 Posting Loads (Tons) – Two-span continuous + ve moments
Span length
20 Ft
40 Ft
80 Ft
120 Ft
T5A Posting Load
26.4
24.8
28.1
31.2
(Tons)
T6A
Posting Load
28.2
25.4
28.3
31.4
(Tons)
T7A Posting Load
31.5
27.0
29.0
31.9
(Tons)
D) Posting Loads – Two Span Continuous Negative Moments
 T4A will produce the lowest posting load of all Formula B vehicles (Table C-60). This
compact truck has the highest moment per unit weight resulting in the lowest posting limit.
 Of the trucks with 5 or more axles, T5A will have the lowest posting load (Fig C-56).
However, the degree of conservatism introduced by using T5A as a single posting load is
dependant on the span length. An adverse impact is seen in the very short spans that are
controlled by wheel loads (see table below).
C-134
TABLE C-66 Posting Loads (Tons) – Two-span continuous - ve moments
Span length
20 Ft
40 Ft
80 Ft
120 Ft
T5A Posting Load
29.2
39.3
31.8
36.3
(Tons)
T6A Posting Load
30.5
39.9
31.9
36.4
(Tons)
T7A Posting Load
32.8
40.0
32.2
36.5
(Tons)
E) Posting Loads – Two Span Continuous Shear
 T4A will produce the lowest posting load of all Formula B vehicles (Table C-61). This
compact truck has the highest moment per unit weight resulting in the lowest posting limit.
 Of the trucks with 5 or more axles, T5A will have the lowest posting load (Fig C-57).
However, the degree of conservatism introduced by using T5A as a single posting load is
dependant on the span length. An adverse impact is seen in the very short spans that are
controlled by wheel loads (see table below).
TABLE C-67 Posting Loads (Tons) – Two-span continuous shear
Span length
20 Ft
40 Ft
80 Ft
120 Ft
T5A Posting Load
24.1
25.2
32.4
35.7
(Tons)
T6A Posting Load
26.7
26.9
33.2
36.2
(Tons)
T7A
Posting Load
28.9
29.0
34.1
36.7
(Tons)
Live Load Reactions -- Transverse Members
 Truck T7A has the highest live load reaction on transverse members for stringer spans from
10 ft to 30 ft (Table C-62). Truck BFT reactions are within 5% of the truck T7A values and
may be used as a single rating vehicle for screening purposes.
 Truck T4A has the highest wheel reaction on transverse members per unit weight (Fig C-58)
and will result in the lowest posting. Truck T5A will have the next lowest posting.
 This shows that like longitudinal members, the posting of transverse members will also be
governed by the four and five axle trucks.
C-135